Abstract:
A dynamic mechanical analyzer and a sample fixture for a dynamic mechanical analyzer that attaches fixed clamps in the sample fixture to a rigid frame using mounts that are compliant in the direction perpendicular to the sample displacement but which at the same time are resistant to rotation about the transverse direction of the sample. The compliant mounts include a pair of flexures that are attached to each fixed clamp and to the frame of the sample fixture. In an embodiment, the pair of flexures are thin flat members such that each pair constitutes two parallel leaf springs. The flexures flex to allow the fixed clamps to move perpendicularly to the sample displacement, but at the same time prevent rotation of the fixed clamps.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a U.S. National Stage of International Application No. PCT/US2014/068493, filed Dec. 4, 2014, which claims priority to and the benefit of U.S. Provisional Application No. 61/916,434, filed Dec. 16, 2013, the contents and teachings of all of which are hereby expressly incorporated by reference in their entireties. 
     
    
     BACKGROUND 
       [0002]    The embodiments disclosed herein relate to dynamic mechanical analyzers (DMAs) and to sample fixtures for use in DMAs. Dynamic mechanical analysis is a material characterization method which exposes a sample to a periodic force and measures the resulting displacement. A dynamic mechanical analyzer measures the phase between the applied force and the resulting displacement of the sample, and uses this measurement to separate the force into a viscous and an elastic component. The elastic component is the displacement energy that is stored in the sample while the viscous component is the displacement energy that is lost via viscous dissipation. 
         [0003]    In many DMAs, the instrument typically displays the elastic and viscous components as the storage modulus and the loss modulus. Experiments are generally performed over a range of temperatures or over a range of frequencies to measure temperature-dependent or frequency-dependent material characteristics, respectively. The glass transition is an important temperature and frequency dependent material characteristic that is often measured using dynamic mechanical analysis. In this transition, an amorphous or glassy material becomes more flexible or rubbery, typically as temperature increases. DMAs typically detect the glass transition as a sharp decrease in the storage modulus and an attendant increase in the loss modulus. 
         [0004]    DMAs may subject samples to different deformation modes, including tension, compression, shear and flexure. The tension mode is typically employed for analysis of samples with very small cross sectional areas such as thin films or fibers. The compression mode is most often used for analysis of very soft materials such as foams. FIGS. 8 and 11 of U.S. Pat. No. 5,710,426, which is incorporated by reference herein, show examples of tension and compression fixtures. Samples may be deformed in shear using torsion fixtures or parallel plate shearing fixtures. FIG. 12 of U.S. Pat. No. 5,710,426 shows an example of a parallel plate shearing mode fixture. Flexural deformation mode is commonly used for samples such as composites that are very stiff. Flexure modes include 3-point bending, 4-point bending and single and double cantilever modes. FIGS. 9 and 10 of U.S. Pat. No. 5,710,426 show examples of 3-point bending and double cantilever fixtures. In single and double cantilever modes, the ends of the sample are fixed to prevent rotation, causing the sample to develop an s curve when displaced. 
         [0005]    In the cantilever flexure modes, the samples are generally parallelepipeds having a rectangular cross section that is usually wider than it is thick, i.e. the thin dimension is oriented parallel to the displacement direction. To obtain accurate measurements of the moduli, the ends of the sample must be rigidly clamped to prevent any rotation; even very small rotations may result in substantial errors in measured moduli. The fixtures of FIG. 9 of U.S. Pat. No. 5,710,426 achieve this for double cantilever mode by using a rigid closed frame that joins the clamping surfaces of the two fixed ends together. While this design is very effective at preventing rotation of the ends of the sample, it has the disadvantage of constraining the sample, preventing its expansion and contraction as it is heated or cooled. This causes thermal stresses and strains to develop in the sample that cause errors in the measured moduli. 
         [0006]    One fixture that reduces thermal expansion and contraction strains uses a single cantilever mode in which the sample is clamped at one end and the opposite end is clamped by the moving fixture. This has the disadvantage that the moving fixture is attached to the DMA drive rod and depends on the stiffness of the drive rod and fixture attachment to prevent rotation. However, it often does not adequately prevent rotation of the moving end of the sample, especially when stiff samples are measured. This reduces the accuracy of the measured stiffness and hence the moduli. This method is only suitable for samples having low stiffness, which are less likely to experience rotation of the moving end of the sample. 
         [0007]    Another approach for reducing thermal expansion strains is disclosed in U.S. Pat. No. 4,967,601, which is incorporated by reference herein. This patent discloses a resilient sample holder that can move in a direction perpendicular to the displacement of the sample to accommodate the sample thermal expansion and contraction. The fixed ends of the sample fixtures are mounted to flexible arms whose bending characteristics allow the sample fixtures to move. The flexibility of these arms also reduces the resistance to rotation of the fixed ends of the sample fixtures, introducing similar errors to the single cantilever fixtures. 
         [0008]    Yet another means for reducing thermal expansion strains is disclosed in U.S. Pat. No. 4,730,498, which is incorporated by reference herein. This patent discloses a double cantilever fixture having the fixed ends mounted on carriages that allow them to move readily in a direction perpendicular to the displacement of the sample to accommodate sample thermal expansion and contraction. However, this fixture is quite massive and requires bearings that must operate with very low friction even at elevated temperatures. The massive fixture may create large temperature lags, which could adversely affect sample measurement accuracy. 
       SUMMARY 
       [0009]    This summary is intended to provide an overview of the subject matter of the present invention, and is not intended to identify essential features or key elements of the subject matter, nor is it intended to be used to determine the scope of the claimed invention. The proper scope of the invention may be ascertained from the detailed description of the embodiments provided below, the figures referenced therein and the claims. 
         [0010]    Embodiments of the sample fixture for use in DMAs described herein use the double cantilever displacement mode while avoiding the disadvantages inherent in the references described above. The embodiments disclosed herein provide rigid mountings for the fixed clamps that readily accommodate thermal expansion and contraction of the sample. They avoid the complications of bearings, springs and carriages. They also have a low mass, which keeps the heating and cooling load low and keeps temperature lags small during controlled heating and cooling experiments. 
         [0011]    The DMA sample fixtures disclosed herein attach the fixed clamps to a rigid frame using mounts that are compliant in the direction perpendicular to the sample displacement but which at the same time are resistant to rotation about the transverse direction of the sample. The compliant mounts comprise a pair of flexures that are attached to the each fixed clamp and to the clamp frame. In an embodiment, the pair of flexures are thin flat members such that each pair constitutes two parallel leaf springs. The flexures flex to allow the fixed clamps to move perpendicularly to the sample displacement, but at the same time prevent rotation of the fixed clamps. 
         [0012]    An embodiment is a dynamic mechanical analyzer (DMA) that has a frame supporting air bearings, and a linear permanent magnet motor. The linear permanent motor has a fixed permanent magnet and a moving coil, and is attached to the frame. It also has a slide attached to the moving coil. Current applied to the coil causes the moving coil to apply a drive force to the slide. The air bearings guide the slide so that it moves only along one direction. A drive rod is attached to one end of the slide. The DMA also has a sample fixture. The sample fixture includes a frame fixture, a moving clamp attached to the other end of the drive rod, a first fixed clamp attached to the frame fixture by a first pair of flexures; and a second fixed clamp attached to the frame fixture by a second pair of flexures. The sample fixture is configured to hold a sample between the first fixed clamp and the second fixed clamp, and the moving clamp is configured to hold the sample at a position between the first fixed clamp and the second fixed clamp. 
         [0013]    Another embodiment is a sample fixture that has fixture frame, a first fixed clamp attached to the fixture frame by a first pair of flexures and a second fixed clamp attached to the fixture frame by a second pair of flexures. The first fixed clamp is configured to engage a sample at a first end of the sample and the second fixed clamp is configured to engage the sample at a second end of the sample. The sample fixture also has a moveable clamp configured to engage the sample at a point between the first fixed clamp and the second fixed clamp. 
         [0014]    Yet another embodiment is a sample fixture for a dynamic mechanical analyzer that has a first pair of flexures attached at one end to a first fixed clamp and at another end to a first end of a fixture frame. It also has a second pair of flexures attached at one end to a second fixed clamp and at another end to a second end of the fixture frame. It also has a moveable clamp configured to engage a sample at a point between the first fixed clamp and the second fixed clamp. The moveable clamp is configured to be detachably connected to a drive rod of a dynamic mechanical analyzer. The fixture frame is configured to be rigidly mounted in a dynamic mechanical analyzer. 
         [0015]    In addition to the specific embodiments described herein, other embodiments and/or modifications will be apparent to one of ordinary skill in the art upon examination of the textual description and the drawings in this specification. It is intended that all such additional embodiments and modifications be included within this specification, be within the scope of the embodiments disclosed herein, and be within the scope of the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0016]    The embodiments described herein can best be understood with reference to the following drawings and textual description. The components identified and/or shown in the figures are not necessarily to scale. The emphasis instead is placed upon illustrating the principles of the embodiments. Moreover, in the figures, like reference numerals designate corresponding parts through the different views. 
           [0017]      FIG. 1  is a schematic diagram showing a dynamic mechanical analyzer with an embodiment of the sample fixture. 
           [0018]      FIG. 2  is an axonometric view of an embodiment of the sample fixture. 
           [0019]      FIG. 3  is an exploded view of the sample fixture shown in  FIG. 2 . 
           [0020]      FIG. 4( a )  shows the flexure used in the embodiment of  FIG. 2  in its undisplaced position. 
           [0021]      FIG. 4( b )  shows the flexure used in the embodiment of  FIG. 2  in a displaced position. 
       
    
    
     DETAILED DESCRIPTION 
       [0022]      FIG. 1  is an overall schematic diagram of an example of a dynamic mechanical analyzer  100 .  FIG. 1  shows the frame  101  of the DMA. Frame  101  supports air bearings  103 , which surround slide  108  on four sides and constrain slide  108  to move only along the one axis of DMA  100 . In the embodiment shown in  FIG. 1 , that axis is the vertical axis of the DMA. Diffraction grating  109  is mounted on slide  108 . Optical transducer  110 , which reads optical signals reflected from diffraction grating  109  is mounted on frame  101 . Motor assembly  111 , which includes permanent magnet assembly  112 , is attached to frame  101 . Moving coil assembly  113  is attached to the bottom of slide  108 . Drive rod  114  connects slide  108  to the moving part of sample fixture  200 . Sample fixture  200  is identified by circle  121  in  FIG. 1  and is shown more clearly in  FIGS. 2 and 3 . The nonmoving part of the sample fixture  200  is supported by posts  116 . 
         [0023]    In operation, DMA  100  is used to characterize the sample mounted in sample fixture  200  by moving drive rod  114  in a predetermined direction, typically in an oscillating motion, although other modes of motion may be used. In the embodiment shown schematically in  FIG. 1 , the predetermined direction is the vertical direction. In the embodiment of  FIG. 1 , drive rod  114  is attached to slide  108  at its bottom end and to sample fixture  200  at its top end. The DMA measures the resulting amplitude and phase of the oscillation in the sample mounted in the sample fixture, as a function of the drive force applied to the sample by drive rod  114 . 
         [0024]    The oscillation of drive rod  114  is measured using diffraction grating  109  which is mounted on slide  108 . As slide  108  and diffraction grating  109  move up and down to move sample fixture  200 , the intensity of a beam reflected by diffraction grating  109  and incident on optical transducer  110  is modulated. Optical transducer  110  thus produces a series of pulses as slide  108  and diffraction grating  109  move in the predetermined direction. The DMA then calculates the distance the slide has moved by counting the number of pulses received from the optical transducer. 
         [0025]    Drive rod  114  is connected to the moving clamp of sample fixture  220 , as described below with reference to  FIGS. 2 and 3 . The force applied to drive rod  114  is measured by measuring the DC current that flows through the windings of moving coil assembly  113 , which applies a force to slide  108  and thus to drive rod  114 . The applied force is proportional to the DC current, and its direction corresponds to the polarity of the current. 
         [0026]      FIG. 2  is an axonometric view of a double cantilever dynamic mechanical analysis fixture with laterally compliant fixed sample holders that are restrained against rotation. As shown in  FIG. 2 , sample  201  has the form of a parallelepiped. It is held in place by fixed clamps  202 . Moving clamp  203  engages the sample at midspan between the fixed clamps and is displaced perpendicularly to the span of the sample to deform the sample. Each fixed clamp comprises a clamp base  204 , a movable clamp face  205 , a clamping screw  206 , a crossbar  207  and rods  208 . The rods are affixed to the clamp base and the crossbar is affixed to the ends of the rods opposite the ends that are affixed to the clamp base. The orientation along the length of the sample from one fixed clamp on one side of the sample to the second fixed clamp on the opposite side of the sample will be referred to herein as the “sample orientation.” 
         [0027]    Clamping screw  206  is threaded through the center of the crossbar and engages the movable clamp face driving it against the sample, clamping it against the clamp base. The ends of the movable clamp faces have notches  209  that engage the rods, preventing the moving clamp faces from rotating. Thus, the ends of the sample are held fast by the movable clamp faces against the clamp bases, preventing the ends from rotating. 
         [0028]    Moving clamp  203  comprises a clamp base, a movable clamp face, a clamping screw, a crossbar and rods that can be substantially similar to and perform the same functions as the similar components of the fixed clamps. Dovetail connector  211  is configured to engage a complementary dovetail connector at the top end of a drive rod, such as drive rod  114  shown in  FIG. 1 . The fixture frame  210  is a rigid structure that can be attached to support posts (not shown) in the DMA using, for example, mounting holes  211  in fixture frame  210 . The support posts are in turn connected to the DMA frame and maintain the position of the sample and sample fixtures within a furnace enclosure that controls the experiment temperature and atmosphere. 
         [0029]    Each clamp base  204  is joined to fixture frame  210  by a pair of flexures  212   a  and  212   b.  In an embodiment, the flexures are flat thin parallelepiped members. In an exemplary embodiment, flexures  212   a  and  212   b  are brazed to the outer and inner sides of the end portions of fixture frame  210 . Flexures  212  a and  212   b  can be attached in any other appropriate manner to fixture frame  210 , for example by welding or diffusion bonding, or by using rivets or bolts. The fixtures could also be machined together with the clamp base out of one block. If the measurements are only carried out at relatively low temperatures, adhesives may be used. 
         [0030]    As shown in  FIGS. 2 and 3 , flexures  212   a  and  212   b  have a thin dimension, a length and a width. The thin dimension of the flexures is oriented parallel to the sample orientation, i.e., parallel to the span of the sample. The long dimension of the flexures is oriented parallel to the direction of the sample displacement and the width of the flexures is oriented perpendicular to the direction of the sample displacement and perpendicular to the sample orientation. Thus the long direction of the flexures is parallel to the direction along which the sample would be displaced. Each of the two flat thin flexures is attached by brazing or by another technique at one end to opposite faces of the clamp base that are perpendicular to the clamping surface and at the opposite ends to corresponding inner and outer faces on the frame, as illustrated in  FIGS. 2 and 3 . 
         [0031]    As best shown in the exploded view of the sample fixture in  FIG. 3 , the flexures are attached to the clamp base faces  332   a  and  332   b  and to the fixture frame faces  331   a  and  331   b  continuously over the entire overlapping surfaces by a process such as brazing to ensure that the joints are rigid. This construction completely prevents rotation of the flexures relative to the clamp bases and the frame. Thus, when the clamp bases are displaced parallel to the sample span and perpendicular to the sample displacement, whether by sample thermal expansion or by sample contraction, the flexures will flex in an S-bend, as shown in  FIG. 4( b )  (described below). The clamping faces of the clamp base will remain parallel to each other and perpendicular to the sample orientation. This construction prevents rotation of the ends of the sample. 
         [0032]    The exploded view of sample fixture  300  in  FIG. 3  shows the components of the sample fixture more clearly. It shows how sample  301  may be held in place at both its ends by fixed clamps  302 .  FIG. 3  shows that each of fixed clamps  302  has a clamp base  304 , a moveable clamp face  305 , a clamping screw  306 , a crossbar  307  and rods  308 . Notches  309  at the end of the movable clamp faces  305  engage rods  308  so as to prevent the moving clamp faces  305  from rotating. Fixture frame  310  can be mounted in the DMA by attaching it, for example, to the DMA&#39;s support posts (such as posts  116  shown in  FIG. 1 ) via mounting holes  311 . 
         [0033]      FIG. 3  also includes arrows labeled X, Y and Z which illustrate the directions referred to in this specification. Thus the Z-direction is the direction parallel to the sample displacement—when the sample fixture is installed in a DMA as shown in  FIG. 1 , the Z direction would be parallel to the direction of drive rod  114 . The X-direction is parallel to the length of the sample, and the Y-direction, which is perpendicular to the Z-direction and to the X-direction, is parallel to the width of the sample. 
         [0034]    Also, the term “direction” as used herein, is bi-directional, as indicated by the double arrows in  FIG. 3 . For example, if the Z-direction is vertical, movement in the Z-direction means movement both up and down. If the X-direction is horizontal from the left to the right, movement in the X-direction means movement both to the left and to the right. Movement in the Y-direction also means movement in both directions—in the illustration of  FIG. 3 , it would include movement towards the viewer of the illustration and movement away from the viewer. 
         [0035]    Movable clamp  303  may engage the sample at midspan between fixed clamps  302 . Movable clamp  303  has a clamp base, a movable clamp face, a clamping screw, a crossbar and rods. These components can be similar to and perform the same functions as the corresponding components of fixed clamps  302 . When the sample fixture shown in  FIGS. 2 and 3  is installed in a DMA such as the DMA shown in  FIG. 1 , dovetail connector  321  engages a complementary dovetail connection at the top of a drive rod such as drive rod  114 , shown in  FIG. 1 . 
         [0036]      FIG. 3  most clearly shows the pair of flat flexures  312   a  and  312   b.  The top ends of flexures  312   a  are brazed to outer sides  332   a  of clamp base  304  and the tops ends of flexures  312   b  are brazed to the inner sides  332   b  of clamp base  304 . The bottom ends of flexures  312   a  and  312   b  are brazed to fixture frame  310 , on either side of end portions  322  of fixture frame  310 . Specifically, flexures  312   a  are brazed to the outer sides  331   a  of end portions  322  and flexures  312   b  are brazed to the inner sides  331  b of end portions  322 . 
         [0037]      FIG. 4( a )  shows a flexure in its undisplaced position and  FIG. 4( b )  shows that flexure in a displaced position. Joining ends  404  and  413  of the flexures at the frame end and at the clamp base end forces them to bend in an S-curve when the clamp base is displaced laterally and prevents the clamp base from rotating. 
         [0038]    The flexures are forced to bend in an S-curve because end  413  is brazed to frame end  322  of fixture frame  310  (shown in  FIG. 3 ), and end  404  is brazed to clamp base  304  (shown in  FIG. 3 ). Frame end  322  is fixed because it is part of the fixture frame that is configured to be attached to the DMA. When force F is applied to clamp base  304  by expansion or contraction of the sample, clamp base  304  moves laterally and without rotation. When the sample is displaced by the moving clamp  303 , the ends of the sample in the fixed clamps  302  are prevented from moving in the direction of the moving clamp displacement by the fixed clamps. The fixed clamps are configured to also prevent the ends of the sample from rotating when the sample expands or contracts. 
         [0039]    A moment M that depends on the force exerted by the moving clamp and the sample stiffness is also developed at the fixed clamps. That moment tends to rotate the fixed clamps, but is resisted by flexures  212   a  and  212   b.  Thus one of the flexures is loaded in tension and the other is loaded equally but in compression. The tension and compression forces acting together over the distance they are separated constitute a couple that resists the moment developed in the sample at its clamped end by the sample displacement and by any expansion or contraction of the sample. 
         [0040]    Although the flexures are relatively thin, they still have substantial cross sectional areas and are fairly short. For this reason, the flexures can withstand tension and compression loads with very little displacement, and thereby resist the moment with very little rotation. The flexures may be fabricated, for example, from materials that are oxidation resistant, and can withstand the temperatures they will be subjected to in the DMA without warping or losing their stiffness. For example, the flexures may be fabricated from stainless steel and may be 0.005 to 0.015 inches thick, for example 0.008 inches thick. Their width would typically be on the order of the maximum width of the samples, and their length would generally be selected to fit into the fixture frame. 
         [0041]    On the other hand, the flexures have low lateral stiffness, because they are very thin in the X-direction, which is the direction of the displacement of the fixed clamp. The cross sectional area of the flexures, their length and the modulus of elasticity of the material of construction determines the stiffness of the flexures. The flexures should be fabricated from materials that can operate within their elastic range at maximum lateral displacement. Otherwise the flexures may yield and become permanently deformed. Given that the moment developed in restraining the ends of the sample against rotation puts one of the pair of thin flexures in compression, the combination of length and radius of gyration of the flexures must be chosen to ensure that they do not buckle under the compression load. 
         [0042]    The flexures may be fabricated from stainless steel parallelepipeds or from other materials that have substantially similar mechanical properties, i.e., have substantially similar stiffness, and can operate within their elastic range at the maximum lateral displacement and at the maximum and minimum temperatures anticipated during operation of the DMA. 
         [0043]    Although only one embodiment of the sample fixture has been described in detail in this specification, other embodiments, structures and features will be apparent to one of ordinary skill in the art upon examination and study of the detailed description and the accompanying figures. It is intended that all such additional embodiments, structures and features be included within this disclosure, be within the scope of the embodiment described herein, and be protected by the claims set forth below.