Column

Material failure at the MEMS scale- Size effects on fracture behavior -Kazuki Takashima, Professor, Kumamoto University Graduate School of Scienceand Technology, Materials Science and Engineering
where metal is used for parts in which bending (as seen incantilevers and hinges), and twisting stress is applied, this size
effect becomes important.
Incidentally, for the design and development of MEMS
devices with superior reliability and durability, it is very
important to evaluate the rupture characteristics of
microdimensional materials with high precision. Here I will
present a relevant example of a size effect. When uniform force
is applied to the material, stress is concentrated at the ends ofany scratches or cracks. However, if the stress at the end of acrack exceeds the yield stress, plastic deformation will occur. If
the size of the area where this plastic deformation occurs (inthe case of failure, the parameter related to characteristiclength) is very small compared to the ligament length (thelength from the end of the crack to the free surface beyond it)brittle fracture will occur. However, if the size of the area islarge, a size effect appears in which the fracture morphology ofthe material transitions from brittle fracture to ductile fracture.
In ductile materials, the characteristic length in this case is in
the order of millimeters or higher, so even if the size is reduced
to micron order, the material still tends towards ductile
fracture. However, in brittle materials, the fracture morphology
may make a transition according to the size. In our group, we
researched the fracture behavior from micro to macro sizes
using single crystals of Fe-3%Si alloy (a material in whichcleavage (brittle) fracture occurs at macro sizes, but with acharacteristic length in the order of 10 µm or more). From ourtests we discovered that although cleavage fracture occurs at
the macro size, the behavior changes to ductile fracture at themicro size (Fig. 1).
In MEMS, in order to aim for higher performance it isconsidered necessary to use many materials such as metals,ceramics, polymers and so on, and as well as silicon materials.
Furthermore, because there are many types of silicon andceramic that undergo brittle fracture at macro sizes, I believethat our results showing the effects of dimension on fracture
behavior will prove very important in designing MEMS devices
that are reliable and durable.

Since beginning research several years ago regarding
evaluation of mechanical properties of the micromaterials usedin MEMS, I have begun to dip a toe into the world of MEMS.
Whenever I make a presentation about evaluating themechanical properties of micro scale materials, I am always
asked, “What about the size effect?”. Size effect is generally
used to mean the changes in material properties compared withbulk materials when the dimensions of a material are madesmaller. But for those of us who have been involved mainly inmechanical characteristics, the question of how the mechanicalcharacteristics change is what seems to interest us.
Generally it is said that brittle materials (such as glass andceramic) increase in strength as their size gets smaller. Thisphenomenon is explained as being linked to the existing
probability of defects being present in the material. In otherwords, as the dimensions of the material get smaller, so thenumber of defects included in the material becomes fewer,
meaning that the starting points for failure are reduced, thereby
raising the strength. However, with MEMS materials, thedimensions are in the order of microns, so that various othersize effects come into play.
These size effects can be divided into intrinsic effects andextrinsic effects. Intrinsic effects are those where, as thedimensions become smaller, the deformation mechanisms of thematerials change, with the result that the mechanical properties
change. Extrinsic effects are those where the mechanicalproperties change due to exogenous elements such as thedefects mentioned above. With MEMS materials especially, evennanosize defects may be located in stress concentration zones,
causing the mechanical properties of the material to change
significantly. With the materials used for MEMS, the changes in
the mechanical properties caused in the manufacturing process
can be said to be extrinsic size effects since the form of defects
and their existing percentage depends on that process.
However, because both types of effect are typically present
together, size effects on mechanical properties are extremelycomplicated.
Incidentally, the dimension at which size effects begin toappear irrespective of mechanical characteristics is called the“characteristic length”. When electromagnetic properties orquantum effects are involved, characteristic lengths in thenanometer order are typical. However, among mechanicalcharacteristics there are some with a characteristic length in
the micron order which is the size of MEMS. For example,tension tests of ductile materials (materials that show
significant plastic deformation until they break, like many metalmaterials) indicate that material strength largely does notdepend on the dimensions of the material down to the micronsize. However, if a stress gradient or strain gradient occurs suchas with bending or twisting, a size effect becomes apparent inwhich the strength increases as the dimensions of the material
decreases, as demonstrated experimentally and theoretically.
There are differences between the types of material,
particularly with metal materials. However when thecharacteristic length is in the micron order, in MEMS devices

(b)

(a)
Notch

Crack Growth
Direction[010][001]5 m

500 m

Fig.1 Changes in fracture behavior in (a) a macro size
specimen, and (b) a micro size specimen of Fe3%Si single crystal. At macro sizes, cleavage(brittle) fracture occurs, but at micro sizes,
ductile fracture occurs. As this demonstrates,
the fracture behavior and morphology of asingle material differs when the dimensions of
the material change to a micro order.

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