Patent Publication Number: US-2021190606-A1

Title: Strain gages and methods for manufacturing thereof

Description:
FIELD OF INVENTION 
     The present application relates generally to strain gages, and, more particularly to strain gages having a modified coefficient of thermal expansion. 
     BACKGROUND 
     A strain gage can be attached to an object (e.g., a substrate) with an adhesive in order to measure a strain applied to the object. Most of the time, a strain gage and an object to which the strain gage will be attached are made from different materials. Therefore, the coefficient of thermal expansion (CTE) of the strain gage and the CTE of the object are not identical. In that case, a stress will be developed in the glue-line between the strain gage and the object if the environmental temperature changes. This is particularly relevant if the adhesive is a room temperature curing epoxy and strain measurement is performed at elevated temperature. 
     SUMMARY 
     The present application discloses strain gages and methods for manufacturing the strain gages which substantially solve one or more existing technical problems due to limitations and disadvantages of the related art. 
     According to an embodiment of the present application, a strain gage comprises: a flat metallic element; a first layer, wherein the flat metallic element is laminated onto a first surface of the first layer and the flat metallic element covers a first part of the first surface of the first layer; and a second layer laminated onto a second surface of the first layer, wherein the second surface is opposite to the first surface, and a coefficient of thermal expansion (CTE) of the second layer is greater than a threshold value. 
     According to another embodiment of the present application, a method for manufacturing a strain gage comprises: preparing a flat metallic element and a first layer; laminating the flat metallic element onto a first surface of the first layer wherein the flat metallic element covers a first part of the first surface of the first layer; and preparing and laminating a second layer onto a second surface of the first layer, wherein the second surface is opposite to the first surface, and a coefficient of thermal expansion (CTE) of the second layer is greater than a threshold value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING(S) 
         FIG. 1  illustrates a top cross-section view of a strain gage according to an embodiment of the present application; 
         FIG. 2  is a side view of the strain gage shown in  FIG. 1 ; 
         FIG. 3  is a side cross-section view of the strain gage shown in  FIG. 1  which has been installed onto an object; 
         FIG. 4  illustrates a scenario in which a thermal expansion of a strain gage according to an embodiment of this application is equal to a thermal expansion of an object onto which the strain gage has been installed; 
         FIG. 5  illustrates a scenario in which a thermal expansion of a strain gage according to an embodiment of this application is greater than a thermal expansion of an object onto which the strain gage has been installed; 
         FIG. 6  illustrates a scenario in which a thermal expansion of a strain gage according to an embodiment of this application is less than a thermal expansion of an object onto which the strain gage has been installed; 
         FIG. 7A  is a schematic drawing illustrating a layer structure of the strain gage along dotted line I-I′ shown in  FIG. 2 ; 
         FIG. 7B  is another schematic drawing illustrating a layer structure of the strain gage along dotted line I-I′ shown in  FIG. 2 ; 
         FIG. 7C  is a side cross-section view of the strain gage along dotted line I-I′ shown in  FIG. 2 ; and 
         FIG. 8  is a flow chart illustrating a method for manufacturing a strain gage according to an embodiment of this application. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In order to make those objects, technical solutions and advantages of the present application more apparent, some exemplary embodiments according to the present application will be described in detail below with reference to accompanying drawings. It should be noted that the described embodiments are only a part of the embodiments of the present application, and are not to be construed as to be limiting to the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments described herein without departing from the scope of the present application are intended to fall within the scope of this application. In the present description and the drawings, the same reference numerals will be used to represent substantially the same elements and functions, and the repetitive description of these elements and functions will be omitted. In addition, descriptions of elements, functions and configurations well known in the art may be omitted for clarity and conciseness. 
     A strain gage  100  according to an embodiment of the present application will be described with reference to  FIGS. 1-6  and  FIGS. 7A-7C . It will be appreciated that a “strain gage” may also be referred to as a “strain gauge.” 
       FIG. 1  is a top cross-section view of the strain gage  100 .  FIG. 2  is a side view of the strain gage  100  shown in  FIG. 1 . As shown in  FIG. 1  and  FIG. 2 , the strain gage  100  may comprise a metallic element  150 . The metallic element  150  may be formed within the strain gage  100  with a certain pattern (e.g., a serpentine pattern shown in  FIG. 2 ). The metallic element  150  will be described in detail later. 
       FIG. 3  is a side cross-section view of the strain gage  100  which has been installed onto a test object  200  through an adhesive  300  (also may be referred to as glue-line  300 ). As shown in  FIG. 3 , the strain gage  100  according to the present application can be installed onto a test object  200  through an adhesive  300  in order to measure an external force f 0  applied to the test object  200 . The test object  200  may be any of a variety of materials, such as various metals (e.g. steel, stainless steel, aluminum, etc.), various ceramics (e.g. aluminum oxide, titanium silicate, silicon carbide, etc.), and various plastics (e.g. acrylic, polycarbonate, polyvinyl chloride, etc.). As such, the test object  200  may have a variety of temperature-expansion characteristics, i.e. coefficient of thermal expansion (CTE), depending upon the particular material selected. 
     A stress may be developed in the glue-line  300  between the strain gage  100  and the test object  200  because of changes in environmental temperature. For example, when the environmental temperature rises, the test object  200  expands in a horizontal direction shown in  FIG. 3 . Similarly, for the same rise in environmental temperature, the strain gage  100  expands in a horizontal direction. If the expansion of the test object  200  and the expansion of the strain gage  100  in response to rise in environmental temperature are not the same magnitude, then a stress will be developed in the glue-line  300 . 
     It will be appreciated that the above examples of the test object  200  are not intended to be exclusive or be limiting to different scenarios where the strain gage  100  may be applied. In the following description, unless indicated otherwise, a metal substrate will be taken as an example of the test object  200 . 
     As briefly discussed above, a stress may exist in the glue-line between a strain gage and a test object. Different scenarios in which this kind of stress may exist will be illustrated with reference to  FIGS. 4-6 . 
     A strain gage and a test object may be manufactured from the same material, and thus their thermal expansions are the same. That is, the strain gage and the test object may have the same CTE. 
     For example, as shown in  FIG. 4 , a CTE of a strain gage  100  is the same as a CTE of a test object  200 . Therefore, when the environmental temperature rises, the strain gage  100  and the test object  200  have the same thermal expansion (i.e., the same thermal expansion rate). That is, those dotted boxes at the left end of both the strain gage  100  and the test object  200  have the same length in horizontal direction (i.e., L=L′). Similarly, those dotted boxes at the right end of both the strain gage  100  and the test object  200  have the same length in horizontal direction. In this scenario, the glue-line stress is neutral. 
     In some scenarios, the strain gage  100  and the test object  200  shown in  FIG. 4  may be manufactured from different materials, but they may still share the same or a similar CTE. For example, the strain gage  100  may be manufactured from multiple materials (e.g., metals and resins), and the strain gage  100  may have a CTE, as a whole, less than a CTE of resins and meanwhile greater than a CTE of metals. Similarly, the test object  200  may be a metal substrate manufactured from multiple metal alloys, and the test object  200  may have a CTE, as a whole, less than a CTE of some of the metal alloys and meanwhile greater than a CTE of other metal alloys. 
     It will be appreciated that the scenario shown in  FIG. 4  may only happen in an ideal condition. Most of time, a strain gage and a test object do not share the same CTE, and thus the glue-line stress is not neutral. Typically, a strain gage may be manufactured from materials different from those used to manufacture a test object, and thus they may have different thermal expansions. 
     For example, as shown in  FIG. 5 , a CTE of a strain gage  100  is greater than a CTE of a test object  200 . Therefore, when the environmental temperature rises, the strain gage  100  and the test object  200  have different thermal expansions (i.e., different thermal expansion rates). That is, the dotted box at the left end of the strain gage  100  has a length in horizontal direction greater than that of the dotted box at the left end of the test object  200  (i.e., L&gt;L′). Similarly, the dotted box at the right end of the strain gage  100  has a length in a horizontal direction greater than that of the dotted box at the right end of the test object  200 . In this scenario, the glue-line stress is in compression. 
     For another example, as shown in  FIG. 6 , a CTE of a strain gage  100  is less than a CTE of a test object  200 . Therefore, when the environmental temperature rises, the strain gage  100  and the test object  200  have different thermal expansions (i.e., different thermal expansion rates). That is, the dotted box at the left end of the strain gage  100  has a length in horizontal direction less than that of the dotted box at the left end of the test object  200  (i.e., L&lt;L′). Similarly, the dotted box at the right end of the strain gage  100  has a length in horizontal direction less than that of the dotted box at the right end of the test object  200 . In this scenario, the glue-line stress is in tension. 
     It should be noted that although the strain gage  100  and the test object  200  have different thermal expansions as shown in  FIGS. 5-6 , this difference may still be within a desired range at the temperature which strain measurements are made. That is, the CTE difference between the strain gage  100  and the test object  200  is not of sufficient magnitude over the temperature range of strain measurement to exceed the strength of the adhesive in the glue-line  300 . The glue-line stress shown in  FIGS. 5-6  will not exceed the strength of the adhesive as long as the CTE difference is within the desired range at the temperature which strain measurements are made. The strain gage according to the present application may be used to reduce the above-mentioned glue-line stress, thereby both preventing the glue-line adhesive from being damaged by the glue-line stress and thereby improving accuracy of its measurement. The description below with reference to  FIGS. 7A-7C  will describe how to maintain this difference within the desired range. 
     Preferably, the desired range of the CTE difference between the strain gage  100  and the test object  200  may be a range from approximately −3×10 −6 /° F. to approximately 3×10 −6 /° F. This is particularly true for a room temperature curing adhesive  300  used to attach a strain gage to a test object for strain measurement at elevated temperature of approximately 400° F. The lower end of the range (i.e., approximately −3×10 −6 /° F.) means that the CTE of the strain gage  100  is 3×10 −6 /° F. lower than the CTE of the test object  200 . This lower end of the range approximately corresponds to the scenario shown in  FIG. 6 . The higher end of the range (i.e., approximately 3×10 −6 /° F.) means that the CTE of the strain gage  100  is 3×10 −6 /° F. higher than the CTE of the test object  200 . This higher end approximately corresponds to the scenario shown in  FIG. 5 . 
       FIGS. 7A-7C  illustrate the strain gage  100  according to an embodiment of this application. 
       FIG. 7A  and  FIG. 7B  are schematic drawings illustrating a layer structure of the strain gage  100  along dotted line I-I′ shown in  FIG. 2 . It will be appreciated that the space between two different components shown in  FIGS. 7A and 7B  is only intended to show a layer structure of the strain gage  100  from a cross section perspective, and in the strain gage  100 , those components are stacked together as shown in  FIG. 7C .  FIG. 7C  is a side cross-section view of the strain gage  100  along dotted line I-I′ shown in  FIG. 2 . 
     As shown in  FIGS. 7A-7C , the strain gage  100  comprises: a flat metallic element  150 ; a first layer  110 , wherein the flat metallic element  150  is laminated onto a first surface  111  of the first layer  110  and the flat metallic element  150  covers a first part of the first surface  111  of the first layer  110 ; and a second layer  120  laminated onto a second surface  112  of the first layer  110 , wherein the second surface  112  is opposite to the first surface  111 , and a CTE of the second layer  120  is greater than a threshold value. The above-mentioned components of the strain gage  100  will be described in detail as follows. 
     The flat metallic element  150  may be a strain sensitive metallic element. The flat metallic element  150  is a crucial component which may be used to measure a strain corresponding to an external force applied to the strain gage  100 . 
     When an external force (e.g., the external force f 0  shown in  FIG. 3 ) is applied to an object  200 , the object  200  will expand along a horizontal direction, thereby causing the strain gage  100  including the flat metallic element  150  to expand in a similar way. Thus, a strain may be caused to the flat metallic element  150 . In other words, the external force f 0  may be transferred from the test object  200  to the flat metallic element  150 . An electrical resistance of the flat metallic element  150  varies with an external force applied. Therefore, as the test object  200  is deformed by the external force f 0 , the flat metallic element  150  is deformed accordingly, causing its electrical resistance to change. Thus, the flat metallic element  150  can be used to convert the external force f 0  into a change in electrical resistance which can then be measured. For example, by measuring the electrical resistance change through a particular circuit such as a Wheatstone bridge, a strain corresponding to the external force f 0  can be obtained. 
     In an embodiment, as shown in  FIG. 2  and  FIGS. 7A-7C , the flat metallic element  150  may be manufactured to be flat in a three-dimensional perspective. A flat strain sensitive metallic element may be helpful to decrease the thickness of the strain gage  100  thereby causing the strain gage  100  to be easier to be attached to the test object  200 . Further, a flat metallic element may increase contact area between the strain gage  100  and the test object  200  thereby causing it to be more sensitive to a strain applied to the test object  200 . 
     The term “flat” mentioned above means that a length of the metallic element  150  in a horizontal direction shown in  FIG. 7A  is greater than a thickness of the metallic element  150  in a vertical direction shown in  FIG. 7A . 
     It will be appreciated that the dimension of the flat metallic element  150  shown in  FIGS. 7A-7C  is not intended to be limiting to a choice of its dimension. The relationship between a length and a thickness of the flat metallic element  150  may vary based on its application scenarios. For example, in an embodiment, a length of the flat metallic element  150  may be 200 times its thickness. In another embodiment, a length of the flat metallic element  150  may be 2500 times its thickness. 
     As shown in  FIG. 2  and  FIG. 7B , the flat metallic element  150  may be a metallic foil, i.e., the flat metallic element may have a flat metallic foil pattern in a horizontal direction. A flat metallic foil may increase the strain sensitivity and the measurement accuracy of the strain gage  100 . Preferably, as shown in  FIG. 7B , the metallic foil  150  has a serpentine pattern. That is, the metallic foil  150  may have a serpentine cross section view in a horizontal direction. 
     It will be appreciated that the metallic foil pattern of the flat metallic element  150  shown in  FIG. 7B  is not intended to be limiting to a choice of the flat metallic element  150 . Any metallic foil pattern suitable to measure a strain applied to the test object  200  may be chosen. For example, the metallic foil may have other patterns available to obtain an electrical resistance change, such as a reticular pattern and a shutter pattern. 
     The flat metallic element  150  may be made from one or multiple alloys which are sensitive to a change of electrical resistance. 
     In an embodiment, the flat metallic element  150  may be made from one or multiple of nickel alloys. In that case, the flat metallic foil  150  may be made from at least one alloy from a group comprising copper-nickel, nickel-chromium, nickel-aluminum, etc. Preferably, the flat metallic foil  150  may be made from at least one of copper-nickel, nickel-chromium or nickel-aluminum. 
     In an embodiment, the flat metallic element  150  may also be made from one or multiple of iron alloys. In that case, the flat metallic element  150  may be made from at least one alloy from a group comprising iron-aluminum, iron-chromium-aluminum, etc. Preferably, the flat metallic foil  150  may be made from at least one of iron-aluminum or iron-chromium-aluminum. 
     In an embodiment, the metallic foil may also be made from one or multiple of platinum alloys. In that case, the flat metallic element  150  may be made from at least one alloy from a group comprising platinum-tungsten, platinum-chromium, etc. Preferably, the flat metallic foil  150  may be made from at least one of platinum-tungsten or platinum-chromium. 
     In an embodiment, the flat metallic element  150  may be made from any combination of multiple alloys mentioned above. For example, the flat metallic element  150  may be made from at least two from a group comprising copper-nickel, nickel-chromium, nickel-aluminum, iron-aluminum, iron-chromium-aluminum, iron-nickel-chromium, platinum-tungsten, platinum-chromium, etc. Preferably, the flat metallic foil  150  may be made from at least two of copper-nickel, nickel-chromium, nickel-aluminum, iron-aluminum, iron-chromium-aluminum, iron-nickel-chromium, platinum-tungsten or platinum-chromium. 
     Although the above-mentioned embodiments describe those alloy materials which may be used to manufacture the flat metallic element  150 , it will be appreciated that they are only described as a way of example, and they are not intended to be exclusive or be limiting to the present application. For example, the flat metallic element  150  may also be made from one or multiple piezoelectric materials. Once an outside force is applied to the strain sensitive metallic element  150 , there will be a piezoelectric effect caused by electrical charges&#39; movements. Then, by measuring an electrical charge change, a strain corresponding to the outside force can be obtained. 
     In the following description, unless otherwise indicated, the above-mentioned metallic foil will be considered as an exemplary embodiment of the flat metallic element  150 . Thus the flat metallic element  150  may also be referred to as the flat metallic foil  150 . 
     A Coefficient of Thermal Expansion (CTE) of the flat metallic foil  150  may vary because of different materials used for manufacturing the flat metallic foil  150 . In an embodiment, a CTE of the metallic foil  150  may have a range greater than or equal to approximately 5×10 −6 /° F. and less than or equal to 12×10 −6  1° F. 
     A thickness of the metallic foil  150  has a range greater than or equal to approximately 0.0001 inch and less than or equal to approximately 0.0005 inch. This range of its thickness is crucial. On the one hand, typically the metallic foil  150  may be thinner than the first layer  110  (described below), and typically the first layer  110 , as a backing, should be thicker than 0.0005 inch in order to obtain enough strength to support other components. On the other hand, if a thickness of the metallic foil  150  is less than 0.0001 inch, it will become relatively fragile and thus cannot withstand a strain applied. It will be noted that a thickness of the flat metallic foil  150  may be determined based on a thickness of the first layer  110  and an overall thickness of the strain gage  100 . The thickness parameters of the first layer  110  and the strain gage  100  will be specifically described below. 
     The metallic foil  150  may be laminated onto the first surface  111  of the first layer  110  and the metallic foil  150  covers a first part of the first surface  111  of the first layer  110 . 
     As shown in  FIG. 7A , the first surface  111  is the top surface of the first layer  110 . However, a layer sequence shown in  FIG. 7A  is only illustrated as an example of the strain gage  100 . It will be appreciated that the first surface of the first layer  110  may be either its top surface or its bottom surface. If the first surface of the first layer  110  is its bottom surface, then a layer sequence of the strain gage will be reversed accordingly with respect to the layer sequence shown in  FIG. 7A . 
     The first part of the first surface  111  may be a part covered by the flat metallic foil  150 . Accordingly, an area of the first part of the first surface  111  may be equal to an area of a surface of the flat metallic foil  150 . A shape of the first part of the first surface  111  may be the same as a shape of the surface of the metallic foil  150 . For example, as shown in  FIG. 2  and  FIG. 7B , the metallic foil may have a serpentine shape. Accordingly, the first part of the first surface  111  also may have the same serpentine shape. 
     The first layer  110  will be described with reference to  FIGS. 7A-7C  as follows. 
     As shown in  FIGS. 7A-7C , the first layer  110  may be a backing of the strain gage  100 . The backing of the strain gage  100  may be used to support the metallic foil  150  laminated onto the backing. 
     The first layer  110  may be an electrically insulating plastic layer. For example, the first layer  110  may be made from one or multiple resin materials. In an embodiment, the first layer  110  may be made from at least one resin material from a group comprising polyimide, polyester, fiber-reinforced epoxy, polyether ether ketone, etc. Preferably, the first layer  110  may be made from at least one of polyimide, polyester, fiber-reinforced epoxy or polyether ether ketone. The above exemplary resin materials are not intended to be exclusive or be limiting to the present application. The first layer  110  may be made from any one or multiple resin materials which can help to obtain the first layer  110  according to an embodiment of this application. 
     The first layer  110  may be a glass layer which is electrically insulating. In an embodiment, the first layer  110  may be made from at least one material from a group comprising quartz, zinc oxide, tin oxide, magnesium oxide, carbonate, etc. Preferably, the first layer  110  may be made from at least one of quartz, zinc oxide, tin oxide, magnesium oxide or carbonate. The above exemplary materials for the glass layer are not intended to be exclusive or be limiting to the present application. The first layer  110  may be made from any one or multiple materials which can help to obtain the first layer  110  according to an embodiment of this application. 
     A thickness of the first layer  110  may be greater than the thickness of the flat metallic foil  150  mentioned above. In an embodiment, the thickness of the first layer  110  has a range greater than or equal to approximately 0.0005 and less than or equal to approximately 0.005 inch. In other words, the thickness of the first layer  110  may be at least 5 times the thickness of the flat metallic foil  150 , and may be at most 50 times the metallic foil&#39;s thickness. 
     This thickness range of the first layer  110  may be crucial. On the one hand, the least thickness of the first layer  110  (i.e., at least 5 times the thickness of the flat metallic foil  150 ) may make it possible to offset an expansion difference in a vertical direction between the first layer  110  and the flat metallic foil  150 . On the other hand, the first layer  110  (with a thickness of at most 50 times the thickness of the flat metallic foil  150 ) may help to transfer the external force f 0  mentioned above to the flat metallic foil  150  timely and accurately, and also help to maintain a relatively small size of the strain gage  100 . 
     A Coefficient of Thermal Expansion (CTE) of the first layer  110  may vary because of different materials used for manufacturing the first layer  110 . In an embodiment, a CTE of the first layer  110  may have a range greater than or equal to approximately 10×10 −6 /° F. and less than or equal to 70×10 −6 /° F. 
     Preferably, the combined CTE of the metallic foil  150  and the first layer  110  may be close to or the same as that of the test object  200 . The closer they are the smaller the magnitude of the stress developed in the glue-line upon a change in environmental temperature. Therefore, the materials of the metallic foil  150  and the first layer  110  may be predetermined by a test object which the strain gage  100  will be attached to. For example, if the strain gage  100  will be attached to a metal substrate (e.g., an aluminum surface of a metal device), then the combined CTE of the metallic foil  150  and the first layer  110  may be predetermined to be approximately 13×10 −6 /° F. 
     It will be noted that typically, there are three types of thermal expansion: linear expansion, volume expansion and area expansion. Here in this application, although as an environmental temperature changes the test object  200  may accordingly change its volume and surface area as well, those volume and surface area changes may be ignored. Further, because the metallic foil  150  is flat and attached to the test object  200  to measure a strain caused by the external force f 0  in a horizontal direction shown in  FIG. 3 , the measurement will be merely focusing on a linear expansion in the horizontal direction. Therefore, the thermal expansion in this application focuses on a linear expansion. Thus, in the present application, unless otherwise indicated, the terms “thermal expansion” and “linear expansion” are interchangeable. Accordingly, the term “CTE” represents a coefficient of linear expansion. 
     An elastic modulus of the first layer  110  may vary because of different materials used for manufacturing the first layer  110 . In an embodiment, the elastic modulus of the first layer  111  has a range greater than or equal to approximately 0.5×10 6  pounds per square inch (PSI) and less than or equal to approximately 5×10 6  PSI. 
     It will be noted that typically there are three types of elastic modulus: Young&#39;s modulus, shear modulus and bulk modulus. This application mainly addresses a resistance of the strain gage  100  to be deformed elastically in a horizontal direction shown in  FIG. 3  when an external force is applied to it. Therefore, shear modulus and bulk modulus are not parameters which should be considered for manufacturing the strain gage  100  according to this application. Thus, in this application, unless otherwise indicated, the terms “elastic modulus” and “Young&#39;s modulus” are interchangeable. 
     A third layer  130  in the strain gage  100  will be described with reference to  FIGS. 7A-7C  as follows. 
     As shown in  FIGS. 7A-7C , the third layer  130  is coated on the flat metallic foil  150  and a second part of the first surface  111  of the first layer  110 . The third layer  130  may be used to protect the other components under it. 
     In one embodiment, the third layer  130  may be a film layer. For example, the third layer  130  may be made from at least one material from a group comprising silicon nitride, silicon oxide, etc. Preferably, the third layer  130  may be made from at least one of silicon nitride or silicon oxide. 
     In another embodiment, the third layer  130  may be a plastic layer protecting the other components in the strain gage  100 . For example, the third layer  130  may be made from a resin material or multiple resin materials. In an embodiment, the third layer  130  may be made from at least one material from a group comprising polyimide, polyester, fiber-reinforced epoxy, polyether ether ketone, etc. Preferably, the third layer  130  may be made from at least one of polyimide, polyester, fiber-reinforced epoxy or polyether ether ketone. 
     It will be appreciated that the above-mentioned materials for the third layer  130  are not intended to be exclusive or be limiting to the present application. The third layer  130  may be manufactured from any materials as long as those materials are suitable to protect those components under the third layer  130 . 
     When manufacturing the strain gage  100 , the third layer  130  will be coated on the first surface  111  of the first layer  110  after the metallic foil  150  has been laminated onto the first surface  111  of the first layer  110 . Therefore, the third layer  130  may not cover all area of the first surface  111 . That is, the third layer  130  may cover two parts: the flat metallic foil  150  and a second part of the first surface  111  (i.e., an area of the first surface  111  not covered by the flat metallic foil  150 ). 
     In one embodiment, the second part of the first surface  111  may cover all area of the first surface  111  not covered by the metallic foil  150  in order to fully protect other components under the third layer  130 . In another embodiment, the second part of the first surface  111  may only cover a part of that area of the first surface  111  not covered by the metallic foil  150  so that only a part of those components under the third layer  130  may be protected. 
     A CTE of the third layer  130  may be greater than or substantially the same as that of the flat metallic foil  150 . In that case, when an environmental temperature changes, the third layer  130  may expand either faster than the flat metallic foil  150  or at the same expanding rate as that of the flat metallic foil  150 . Thus, the third layer  130  may not be broken by an expansion of the flat metallic foil  150 . 
     The third layer  130  may have a CTE slightly less than that of the flat metallic foil  150 . In that case, although the third layer  130  may expand slower than the flat metallic foil  150 , the third layer  130  can still protect the flat metallic foil  150  because of an elasticity of the third layer  130 . 
     In an embodiment, a CTE of the third layer  130  may have a range greater than or equal to approximately 5×10 −6 /° F. and less than or equal to 70×10 −6 /° F. 
     The second layer  120  in the strain gage  100  will be described with reference to  FIGS. 7A-7C  as follows. 
     The second layer  120  may be laminated onto the second surface  112  of the first layer  110 . The second surface  112  is opposite to the first surface  111 , and a CTE of the second layer  120  may be greater than a threshold value. 
     As shown in  FIG. 7A , the second surface  112  of the first layer  110  is the bottom surface of the first layer  110 . However, the relative positions of those surfaces shown in  FIG. 7A  are not intended to be limiting to the present application. The basic principle is that the first surface  111  and the second surface  112  are opposite to each other. In one embodiment, the first surface of the first layer may be the bottom surface of the first layer, and accordingly the second surface of the first layer may be the top surface of the first layer. 
     As shown in  FIG. 7A , the second layer  120  has two surfaces, i.e., a first surface  121  (i.e., a bottom surface of the second layer  120  shown in  FIG. 7A ) and a second surface  122  (i.e. a top surface of the second layer  120  shown in  FIG. 7A ). The first surface  121  of the second layer  120  is opposite to the second surface  122  of the second layer  120 . The second surface  122  of the second layer  120  is attached to the second surface  112  of the first layer  110 . 
     The purpose of laminating the second layer  120  is to modify an overall CTE of the strain gage  100  so that the overall CTE of the strain gage  100  may be closer to that of the test object  200 . Therefore, as environmental temperature changes the stress developed in the glue-line  300  between the strain gage  100  and the test object  200  may be substantially reduced, and thus strains can be accurately measured by the strain gage  100  before the adhesive layer  300  fails from an over stress condition. 
     Typically the strain gage  100  will be attached to a metal device to measure a strain. If the metal device has a high thermal expansion coefficient, then the overall CTE of the strain gage  100  needs to be increased to minimize the stress developed in the glue-line  300  upon an increase in the environmental temperature. Although the second layer  120  is located at a relative lower part in the strain gage  100 , it may have a desirable thickness and a desirable CTE which could correspondingly modify the overall CTE of the strain gage  100 . 
     In an embodiment, the threshold value may be the CTE of the flat metallic foil  150 . That is, the CTE of the second layer  120  may be greater than the CTE of the metallic foil  150 . Further, in this embodiment, the CTE of the second layer  120  may be less than or equal to that of the test object  200 . Since the CTE of the second layer  120  has a range between the CTE of the metallic foil  150  and the CTE of the test object  200 , the second layer  120  may play a transition role between the test object  200  and the strain gage  100  from a linear expansion perspective. That is, the second layer  120  may reduce the stress developed in the glue line upon a change in environmental temperature. 
     It will be appreciated that in the above embodiment, the overall CTE of the strain gage  100  can be increased if the CTE of the second layer  120  is larger than that of the metallic foil  150 . The increased overall CTE of the strain gage  100  may reduce the CTE difference between the strain gage  100  and the test object  200  in order to maintain the CTE difference within the above-mentioned desired range. 
     The CTE of the second layer  120  may not be significantly smaller than that of the test object  200 , because if the CTE of the second layer  120  is significantly smaller than that of the test object  200 , then it would be impossible to increase the overall CTE of the strain gage  100  to reach the lower end of the desired range (e.g., approximately −3×10 −6 /° F.), thereby causing the CTE difference between the strain gage  100  and the test object  200  to go beyond of the desired range described with reference to  FIG. 6 . 
     The CTE of the second layer  120  may not be significantly larger than that of the test object  200 , because if the CTE of the second layer  120  is significantly larger than that of the test object  200 , then the overall CTE of the strain gage  100  might be much larger than the CTE of the test object  200 , thereby causing the CTE difference between the strain gage  100  and the test object  200  to go beyond the desired range (e.g., approximately 3×10 −6 /° F.) described with reference to  FIG. 5 . 
     In an embodiment, the CTE of the second layer  120  may be greater than or equal to that of the flat metallic foil  150  and less than or equal to that of the test object  200 . 
     The threshold value may be the CTE of the first layer  110 . That is, the CTE of the second layer  120  may be greater than CTE of the first layer  110 . 
     Preferably, the threshold value may be 11×10 −6 /° F. That is, the CTE of the second layer  120  may be greater than 11×10 −6 /° F. 
     Preferably, the CTE of the second layer  120  may have a range from 11×10 −6 /° F. to 15×10 −6 /° F. 
     Preferably, the CTE of the second layer  120  may have a range from 12×10 −6 /° F. to 14×10 −6 /° F. 
     Preferably, the CTE of the second layer  120  may be approximately 13×10 −6 /° F. 
     An elastic modulus of the second layer  120  may or may not be equal to that of the flat metallic foil  150 . The second layer  120  may also help to maintain a rigidity of the strain gage  100 . 
     In an embodiment, the elastic modulus of the second layer  120  has a range greater than or equal to approximately 5×10 6  pounds per square inch (PSI) and less than or equal to approximately 40×10 6  PSI. 
     Preferably, the elastic modulus of the second layer  120  is approximately 10×10 6  PSI. 
     A thickness of the second layer  120  may have a range greater than or equal to approximately 0.001 inch and less than or equal to approximately 0.01 inch. In other words, the thickness of the second layer  120  may be at least 10 to 100 times thicker than the metallic foil  150 . 
     The second layer  120  may be made from the same material as the flat metallic element  150 . 
     For example, in an embodiment, the second layer  120  may be made from one or multiple of nickel alloys. In another embodiment, the second layer  120  may also be made from one or multiple of iron alloys. In a third embodiment, the second layer  120  may also be made from one or multiple of platinum alloys. Further, the second layer  120  may be made from any combination of multiple alloys mentioned above. 
     The second layer  120  may be made from a material different from the flat metallic element  150 . For example, in an embodiment, the second layer may be made from at least one metal from a group comprising aluminum, copper, silver, gold, etc. Preferably, the second layer may be made from at least one of aluminum, copper, silver or gold. 
     Although the above-mentioned embodiments describe those materials which could be used to manufacture the second layer  120 , it will be appreciated that they are only described as a way of example, and they are not intended to be exclusive or be limiting to the present application. The second layer  120  may be manufactured from any materials as long as those materials are suitable to obtain the above-mentioned characteristics of the second layer  120 . 
     As shown in  FIGS. 7A-7C , the strain gage  100  may further comprise a fourth layer  140 . The fourth layer  140  may also be used to protect those components above it. The fourth layer  140  will be further described as follows. 
     The fourth layer  140  may be laminated onto the first surface  121  of the second layer  120 . As shown in  FIGS. 7A-7C , the first surface  121  of the second layer  120  is the bottom surface of the second layer  120 . 
     It will be appreciated that in the above description, the first surface  121  and the second surface  122  represent the bottom surface and the top surface of the second layer  120  respectively, and they are not intended to be limiting to the present application. In embodiments, by laminating the second layer  120  onto the first layer  110  and laminating the fourth layer  140  onto the second layer  120 , one surface of the second layer  120  may be attached to the first layer  110 , and another surface of the second layer  120  may be attached to the fourth layer  140 . 
     The fourth layer  140  may be an electrically insulating plastic layer. For example, the fourth layer  140  may be made from a resin material or multiple resin materials. In an embodiment, the fourth layer  140  may be made from at least one from a group comprising polyimide, polyester, fiber-reinforced epoxy, polyether ether ketone, etc. Preferably, the fourth layer  140  may be made from at least one of polyimide, polyester, fiber-reinforced epoxy or polyether ether ketone. 
     The fourth layer  140  may be a glass layer which is electrically insulating. For example, the fourth layer  140  may be made from at least one material from a group comprising quartz, zinc oxide, tin oxide, magnesium oxide, carbonate, etc. Preferably, the fourth layer  140  may be made from at least one of quartz, zinc oxide, tin oxide, magnesium oxide or carbonate. 
     It will be appreciated that the above-mentioned materials which may be used for manufacturing the fourth layer  140  are only described by way of example, and they are not intended to be exclusive or be limiting to the present application. The fourth layer  140  may be manufactured from any materials as long as those materials are suitable to obtain those characteristics of the fourth layer  140  described in this application. 
     In one embodiment, a thickness of the fourth layer  140  has a range greater than or equal to 0.0005 and less than or equal to 0.005 inch. In other words, the thickness of the fourth layer  140  may be at least 1/20 times the thickness of the second layer  120 , and may be at most 5 times the thickness of the second layer  120 . 
     On the one hand, the fourth layer  140 , with at least 1/20 of the thickness of the second layer  120 , may have enough strength for supporting and protecting those components above it. On the other hand, the fourth layer  140 , with at most 5 times the thickness of the second layer  120 , may also help to maintain a relatively small size of the strain gage  100 . 
     In an embodiment, a CTE of the fourth layer  140  may be substantially the same as that of the second layer  120 . In that case, when an environmental temperature changes, the fourth layer  140  may expand at substantially the same expanding rate as that of the second layer  120 . 
     In an embodiment, a CTE of the fourth layer  140  may be relatively greater than that of the second layer  120  and relatively less than that of the test object  200 . In that case, the fourth layer  140  may also be used to modify the overall CTE of the strain gage  100 . In other words, the fourth layer  140  may also play a transition role between the test object  200  and the strain gage  100 . Thus, the fourth layer  140  may also help to reduce a glue-line stress difference by obtaining a CTE difference between the strain gage  100  and the test object  200  within the above-mentioned desired range. 
     A strain gage according to another embodiment of this application will be described as follows. The strain gage according to this embodiment of this application may comprise: a flat metallic element; a first layer, wherein the flat metallic element is laminated onto a first surface of the first layer and the flat metallic element covers a first part of the first surface of the first layer; and a material incorporated into the first layer and used to modify a coefficient of thermal expansion (CTE) of the strain gage to be greater than a threshold value. 
     In this embodiment, flat metallic element is similar to the flat metallic element  150  shown in  FIGS. 7A-7C , and the first layer is similar to the first layer  110  shown in  FIGS. 7A-7C . In this embodiment, the strain gage may further comprise a third layer which is similar to the third layer  130  shown in  FIGS. 7A-7C , and a second layer which is similar to the second layer  120  shown in  FIGS. 7A-7C . 
     The difference between the strain gage described with this embodiment and the strain gage  100  described with reference to  FIGS. 7A-7C  is the material incorporated into the first layer. The material may be used to modify the overall CTE of the strain gage to be greater than a threshold value. 
     Preferably, the material may have a relatively large CTE. When preparing the first layer, the material may be filled or incorporated into the first layer so that a CTE of the first layer may be modified, thereby modifying the overall CTE of the strain gage. The threshold value may be a CTE of the first layer. Preferably, the threshold value may be approximately 11×10 −6 /° F. 
     In an embodiment, the threshold value may have a range similar to or the same as one of those threshold value ranges in the above embodiments mentioned with reference to  FIGS. 7A-7C . 
     For example, the first layer may be a plastic layer made from resin materials. In one embodiment, at least one from a group of metals comprising aluminum, copper, gallium, indium, etc., may be filled into the plastic layer so that a CTE of the first layer may be modified. In another embodiment, at least one from a group of alloys comprising aluminum oxide, zinc oxide, etc., may be filled into the plastic layer. It will be appreciated that the above-mentioned metal materials and alloy materials are not intended to be limiting to the present application. Any material which may be available to modify an overall CTE of the strain gage may be filled or incorporated into it based on the principle of the present application. 
     Preferably, the material may be used to modify a CTE difference between the strain gage and the test object to be within a desired range (e.g., a range from approximately −3×10 −6 /° F. to approximately 3×10 6 /° F. as mentioned above). 
     Preferably, the material may be incorporated into any one of the first layer and the third layer of the strain gage. In another embodiment, the material may be incorporated into both the first layer and the third layer of the strain gage. 
     Preferably, the strain gage may further comprise a second layer. The second layer is laminated onto a second surface of the first layer, wherein the second surface of the first layer is opposite to the first surface of the first layer, and a CTE of the second layer is greater than a CTE of the first layer. The above-mentioned material may also be filled or incorporated in the second layer so that a CTE of the second layer may be used to modify the overall CTE of the strain gage to be greater than a threshold value. Preferably, incorporating the material into the second layer may also help to obtain a desired CTE difference between the strain gage and the test object. 
     It will be appreciated that the material described in the above embodiment may also be used in those embodiments described with reference to  FIGS. 1-7C . For example, the material may be filled or incorporated into any one or any combination of the first layer  110 , the second layer  120 , the third layer  130 , and the fourth layer  140  shown in  FIGS. 7A-7C  for the purpose of modifying the overall CTE of the strain gage  100 . 
     A method for manufacturing a strain gage according to an embodiment of this application will be described with reference to  FIG. 8  together with  FIGS. 1-3  as follows.  FIG. 8  is a flowchart illustrating a method  800  for manufacturing a strain gage according to an embodiment of the present application. 
     As shown in  FIG. 8 , the method  800  comprises: at  801 , preparing a flat metallic element and a first layer; at  802 , laminating the flat metallic element onto a first surface of the first layer wherein the flat metallic element covers a first part of the first surface of the first layer; and at  803 , preparing and laminating a second layer onto a second surface of the first layer, wherein the second surface is opposite to the first surface, and a coefficient of thermal expansion (CTE) of the second layer is greater than a threshold value. The method  800  will be described in detail as follows. 
     It will be noted that the method  800  may be used to manufacture the strain gage  100  shown in  FIGS. 7A-7C . Therefore, unless otherwise indicated, those components mentioned with respect to the method  800  below will be corresponding to those components described above with reference to  FIGS. 7A-7C . 
     At  801 , in an embodiment, preparing a flat metallic element may comprise obtaining the flat metallic element  150  mentioned. The flat metallic element  150  may be one of flat metallic elements existing in the market which may be used to measure a strain. The flat metallic element prepared at  801  may also be any other known or unknown metallic elements which could be used to measure a strain according to the principles of the present application. 
     In an embodiment, preparing a flat metallic element may comprise manufacturing the flat metallic element  150 . At  801 , manufacturing the flat metallic element  150  may comprise any procedure necessary to manufacture a flat metallic element designed for measuring a strain. The present application does not limit those procedures necessary to manufacture a flat metallic element. 
     At  801 , a first layer may also be prepared. In an embodiment, the first layer prepared at  801  may be the first layer  110  mentioned above with reference to  FIGS. 7A-7C . 
     In one embodiment, at  801 , the flat metallic element  150  and the first layer  110  may be prepared at the same time. For example, a manufacturer of the strain gage  100  may manufacture the flat metallic element  150  and the first layer  110  at the same time. In another embodiment, the flat metallic element  150  and the first layer  110  may be prepared in a sequence. For example, the flat metallic element  150  may be manufactured first, and then the first layer  110  may be manufactured. 
     Although the above embodiments describe that the flat metallic element  150  and the first layer  110  may be prepared either at the same time or in a sequence, it will be appreciated that those embodiments are not intended to be exclusive or be limiting to the present application. For example, other components in the strain gage  100  may also be prepared at  801 . In an embodiment, a manufacturer may prepare the flat metallic element  150 , the first layer  110  and other layers (e.g., the second layer  120 ) at the same time or in any desirable sequence. Those processes for preparing other layers will be described below with reference to  FIG. 8 . 
     At  802 , laminating the flat metallic element prepared at  801  onto a first surface of the first layer prepared at  801 , wherein the flat metallic element covers a first part of the first surface of the first layer. 
     The laminating process at  802  may vary depending on types of materials of the flat metallic element and types of materials of a test object onto which the flat metallic element will be laminated. For example, the laminating process at  802  may comprise at least one process from a group comprising heating, pressing, welding, coating, gluing, etc. Preferably, the laminating process at  802  may comprise at least one of heating, pressing, welding, coating or gluing. It will be appreciated that the above-mentioned example of laminating process is not intended to be exclusive and be limiting to the present application. The present application does not limit those processes necessary to the laminating process at  802 . 
     As shown in  FIG. 8 , at  803 , preparing and laminating a second layer onto a second surface of the first layer, wherein the second surface is opposite to the first surface, and a CTE of the second layer is greater than a threshold value. 
     In one embodiment, the second layer prepared at  803  may be the second layer  120  mentioned above with reference to  FIG. 7A . In another embodiment, the second layer prepared at  803  may be any type of metallic layers existing in the market which may be used to modify an overall CTE of the strain gage manufactured by the method  800 . The second layer prepared at  803  may also be any other known or unknown layer with a relatively high CTE which could be used to modify an overall CTE of the strain gage. 
     The laminating process at  803  may vary depending on types of materials of the second layer and types of materials of the first layer onto which the second layer will be laminated. For example, the laminating process at  803  may comprise at least one from a group comprising heating, pressing, welding, coating, gluing, etc. Preferably, the laminating process at  803  may comprise at least one of heating, pressing, welding, coating or gluing. It will be appreciated that the above-mentioned example of a laminating process is not intended to be exclusive and be limiting to the present application. The present application does not limit those processes necessary to the laminating process at  803 . 
     In an embodiment, as shown in  FIG. 8 , the method  800  may further comprise: at  804 , coating a third layer onto the flat metallic element, wherein the third layer covers a second part of the first surface of the first layer prepared at  801 . 
     In one embodiment, the third layer processed at  804  may be the third layer  130  mentioned above with reference to  FIG. 7A . In another embodiment, the third layer processed at  804  may be one of film layers existing in the market which may be used to protect other components in the strain gage. The third layer processed at  804  may also be any other known or unknown protection layer which could be used to protect other components in the strain gage. 
     The coating process may vary depending on types of materials of the third layer and types of materials of the first layer and the flat metallic element onto which the third layer will be coated. For example, the coating process at  804  may comprise at least one process from a group comprising heating, painting, roll-to-roll coating, cooling, etc. Preferably, the coating process at  804  may comprise at least one of heating, painting, roll-to-roll coating or cooling. It will be appreciated that the above-mentioned example of coating process is not intended to be exclusive and be limiting to the present application. The present application does not limit those processes necessary to the coating process at  804 . 
     As shown in  FIG. 8 , the method  800  may further comprise: at  805 , preparing and laminating a fourth layer onto a first surface of the second layer. 
     In one embodiment, the fourth layer processed at  805  may be the fourth layer  140  mentioned above with reference to  FIG. 7A . In another embodiment, the fourth layer processed at  805  may be any plastic layer existing in the market which may be used to support and protect other components in the strain gage. The fourth layer processed at  805  may also be any other known or unknown backing layer which could be used to support and protect other components in the strain gage. 
     The laminating process at  805  may vary depending on types of materials of the fourth layer and types of materials of the third layer onto which the fourth layer will be laminated. For example, the laminating process at  805  may comprise at least one process from a group comprising heating, pressing, welding, coating, gluing, etc. Preferably, the laminating process at  805  may comprise at least one of heating, pressing, welding, coating or gluing. It will be appreciated that the above-mentioned example of laminating process is not intended to be exclusive and be limiting to the present application. The present application does not limit those processes necessary to the laminating process at  805 . 
     It will be appreciated that the terminology used in the present application is for the purpose of describing particular embodiments and is not intended to limit the application. The singular forms “a”, “the”, and “the” may be intended to comprise a plurality of elements. The terms “including” and “comprising” are intended to include a non-exclusive inclusion. Although the present application is described in detail with reference to the foregoing embodiments, it will be appreciated that those foregoing embodiments may be modified, and such modifications do not deviate from the scope of the present application.