Development, modeling and deflection analysis of hybrid micro actuator with integrated thermal and piezoelectric actuation

Micro actuators are irreplaceable part of motion control in minimized systems. The current study presents an analytical model for a new Hybrid Thermo Piezoelectric micro actuator based on the combination of piezoelectric and thermal actuation mechanisms. The micro actuator structure is a double PZT cantilever beam consisting of two arms with different lengths. The presented micro actuator uses the structure of electrothermal micro actuator in which polysilicon material is replaced by PZT. Also the voltage and poling directions are considered in the lengthwise of PZT beams. As a result, the piezoelectric actuation mechanism is based on d ₃₃ strain coefficient. The tip deflection of micro actuator is obtained using Timoshenko beam theory. Analytical results are compared with FEM results along with other reported results in the literature. The effects of geometrical parameters and PZT material constants on actuator tip deflection are studied to provide an efficient optimization of HTP micro actuator.     

Effects of multiple cracking on the residual strength behavior of thermally shocked functionally graded ceramics

When subjected to severe thermal shocks a functionally graded ceramic (FGC) suffers strength degradation due to the thermally-induced damages in the material. Multiple surface cracking has been observed as one of the dominant defects/damages affecting the thermal shock behavior of ceramics. This paper presents a thermo-fracture mechanics model to investigate the thermal shock residual strength behavior of elastically homogeneous but thermally graded FGCs undergoing multiple surface cracking. We consider an FGC plate with an array of parallel edge cracks at the thermally shocked surface. A Fourier transform/superposition method is used to derive the singular integral equation of the thermal shock crack problem. The critical thermal shock that causes crack propagation and thermal shock damage are determined using linear elastic fracture mechanics. The thermal shock residual strength of the FGC as a function of thermal shock severity and crack density (crack spacing) is subsequently evaluated. Numerical calculations are carried out for two FGC materials, i.e., Al₂O₃/Si₃N₄ and TiC/SiC FGCs, to illustrate the effects of crack density (crack spacing) and material gradation on the thermal shock strength behavior of FGCs. It is found that a higher crack density (lower crack spacing) together with appropriately graded material properties significantly enhances the residual strength of the thermally shocked FGCs.     

On the driving force for crack growth during thermal actuation of shape memory alloys

The effect of thermomechanically induced phase transformation on the driving force for crack growth in polycrystalline shape memory alloys is analyzed in an infinite center-cracked plate subjected to a thermal actuation cycle under mechanical load in plain strain. Finite element calculations are carried out to determine the mechanical fields near the static crack and the crack-tip energy release rate using the virtual crack closure technique. A substantial increase of the energy release rate – an order of magnitude for some material systems – is observed during the thermal cycle due to the stress redistribution induced by large scale phase transformation. Thus, phase transformation occurring due to thermal variations under mechanical load may result in crack growth if the crack-tip energy release rate reaches a material specific critical value.     

Interface crack problem in layered orthotropic materials under thermo-mechanical loading

In the present paper, the behavior of an interface crack for a homogeneous orthotropic strip sandwiched between two different functionally graded orthotropic materials subjected to thermal and mechanical loading is considered. It is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically. The main objective of the paper is to study the effects of material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors for the purpose of gaining better understanding of the thermal behavior of graded layer.     

Thermal stress intensity factors for an interface crack in a functionally graded layered structures

The fracture behavior of a functionally graded layered structure (FGLS) with an interface crack under thermal loading is investigated. Considering new boundary conditions, it is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The problem is formulated in terms of a system of singular integral equations. Numerical results are presented to show the influence of the material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors (TSIFs).     

Crack trajectories influenced by mechanical and thermal disturbance in anisotropic material

This work is concerned with the application of the volume energy density criterion for predicting the crack trajectories as influenced by mechanical and thermal disturbance in an anisotropic material. Two-dimensional linear thermoelasticity is employed in conjunction with the well-known complex potentials such that a linear relationship is obtained for the boundary conditions across the crack or line of discontinuity. Boundary collocation is then used to determine the unknown coefficients from which the contours of the volume energy density in the cracked plate can be obtained. The crack path is assumed to coincide with the loci where dilatation would dominate. This corresponds to the locations of relative minimum energy density which can be found by visual inspection. An equal and opposite mechanical stress and thermal gradient are applied on the cracked plate. The former and latter enhance symmetric and asymmetric crack growth, respectively. They would complete depending on the magnitude of the mechanical and thermal load. Numerical results are presented for three (3) different cases of a plate whose principal axes of material symmetry are tilted to the crack plane. The influence of anisotropy on crack path is found to be secondary.     

Crack opening and closure under the action of mechanical and thermal loads

Under general loading conditions, there is no guarantee that the crack surfaces will be fully open. Complete or partial closure of the crack could occur if the surrounding material is compressed. Such a phenomenon is illustrated for the situation of a single crack engulfed by a remote but uniform compressive stress field while tensile forces are applied at isolated points so that the material can counteract against the compressive field. Examples are provided illustrating partial crack closure with or without symmetry about the mid-plane normal to the crack surface. Considered will be mechanical and thermal loadings.     

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.     

Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads

Mixed-mode fracture problems of orthotropic functionally graded materials (FGMs) are examined under mechanical and thermal loading conditions. In the case of mechanical loading, an embedded crack in an orthotropic FGM layer is considered. The crack is assumed to be loaded by arbitrary normal and shear tractions that are applied to its surfaces. An analytical solution based on the singular integral equations and a numerical approach based on the enriched finite elements are developed to evaluate the mixed-mode stress intensity factors and the energy release rate under the given mechanical loading conditions. The use of this dual approach methodology allowed the verifications of both methods leading to a highly accurate numerical predictive capability to assess the effects of material orthotropy and nonhomogeneity constants on the crack tip parameters. In the case of thermal loading, the response of periodic cracks in an orthotropic FGM layer subjected to transient thermal stresses is examined by means of the developed enriched finite element method. The results presented for the thermally loaded layer illustrate the influences of the material property gradation profiles and crack periodicity on the transient fracture mechanics parameters.     

Coupled thermal/mechanical analysis for the fracture of functionally graded materials under transient thermal loading

A comprehensive treatment of fracture of functionally graded materials (FGMs) is provided. It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using a laminated composite plate model to simulate the material non-homogeneity, an algorithm for solving the system based on Laplace transform and Fourier transform techniques is presented. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with arbitrarily varying material properties. Transient thermal stresses are presented. Project supported by the National Natural Science Foundation of China (Nos 10102004 and 19902003).     

Orthotropic semi-infinite medium with a crack under thermal shock

A cracked orthotropic semi-infinite plate under thermal shock is investigated. The thermal stresses are generated due to sudden cooling of the boundary by ramp function temperature change. The superposition technique is used to solve the problem. The crack problem is formulated by applying the thermal stresses obtained from the uncracked plate with opposite sign to be the only external loads on the crack surfaces as the crack surface tractions. The Fourier transform technique is used to solve the problem leading to a singular equation of the Cauchy type. The singular integral equation is solved numerically using the expansion method. The influence of the material orthotropy on the stress intensity factors is shown by comparing the results obtained for different orthotropic materials and isotropic materials in the case of plane stress. The numerical results of the stress intensity factors are demonstrated as a function of time, crack length, location of the crack and the duration of the cooling rate.     

Kinetics of crack formation and growth on the material interface

A model of thermal fluctuation crack formation in aweakened bond region on amaterial interface is proposed. The weakened bond region is modeled by a bridged crack whose properties vary in time according to the thermal fluctuation mechanism. It is assumed that at least one of the materials is a polymer and the crack part occupied by bridges (the end region) is not small compared with the crack length. The stresses in the bridges and the kinetic dependence of the bond density in the crack end region are determined by solving a system of singular integrodifferential equations. The condition for the crack-defect nucleation is the decrease to the critical value of the average bond density on the corresponding part of the weakened bond region. Numerical results permitting one to estimate the crack nucleation time and the typical levels of external loads for the chosen material parameters are presented.     

THERMAL FRACTURE OF FUNCTIONALLY GRADED PLATE WITH PARALLEL SURFACE CRACKS

This work examines the fracture behavior of a functionally graded material （FGM） plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors （TSIFs） at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △Tc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △Tc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △Tc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △Tc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.     

Applicability of the crack faces thermoelectric boundary conditions for thermopiezoelectric materials

The applicability and effect of the crack surfaces thermoelectric boundary conditions in thermopiezoelectric fracture mechanics problem are discussed by using the finite thickness notch approach. The stress and electric displacement intensity factors at the notch tips, and thermal flux and electric displacement inside the notch are derived in closed-form. The numerical results are compared with the ideal crack solutions. It is found that the electrically impermeable crack boundary condition assumption is reasonable if the flaw in the material is a notch with finite width, and the thermal conductivity of air or vacuum inside the crack must be considered.     

Multiple axial cracks in a coated hollow cylinder due to thermal shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing.     

低成本基板倒装焊底充胶分层裂缝扩展研究

采用MIL-STD-883C热循环疲劳加载标准，通过电学检测方法测定了B型和D型两种倒装焊封装焊点寿命。并使用无损声学C-SAM高频超声显微镜技术观测这两种倒装焊封装在焊点有无断裂两种情况时芯片／底充胶界面的分层和扩展，计算得到分层裂缝扩展速率。在有限元模拟中采用粘塑性和时间相关模量描述了SnPb焊点和底充胶的力学行为。使用裂缝尖端附近小矩形路径J积分方法作为断裂力学参量得到不同情况下的界面分层裂缝顶端附近的能量释放率。然后由实验裂缝扩展速率和有限元模拟给出的能量释放率得到可作为倒装焊封装可靠性设计依据的Par—is半经验方程。     

Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth

Background:

Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip.

Objective:

We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading.

Methods:

Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force.

Results:

The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data.

Conclusions:

The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.

     

Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part II: Crack propagation

Propagation behavior of an elliptical crack in thermopiezoelectric material subjected to a uniform temperature is investigated in this paper. The three-dimensional strain energy density formulation is used to determine the direction of crack propagation and the shape of the initial fracture increment. It is found that the elliptical crack grows coplanarly under this particular load case but not normal to the crack front. The elliptical crack tends to become a circular one when thermal loading is applied.     

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

Summary The aim of this work is to investigate the thermal stress intensity factor of a functionally gradient half space with an edge crack under a steady heat flux. All material properties of the functionally gradient half space, except for the coefficient of linear thermal expansion, are exponentially dependent on the distance from the boundary of the plate. The coefficient of linear thermal expansion is assumed to be two-dimensionally dependent. The problem is reduced to a singular integral equation by using the Fourier transform. The thermal stress intensity factor versus the nonhomogeneous material parameters is calculated and represented in figures. The numerical results show that thermal stress intensity factor is dramatically decreased when the material nonhomogeneous parameters are appropriately selected.