A thermomechanical cohesive zone model for bridged delamination cracks

The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction-separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack-bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.     

An analysis of the delamination of an environmental protection coating under cyclic heat loads

A computational analysis of a coated high temperature composite material under cyclic heat flux loading is conducted. The material system considered is a carbon–carbon (CC) composite laminate with a SiC environmental protection coating. Interface crack growth between the CC laminate and the SiC coating as well as the concurrent changes in the effective conductivity of the material system are modeled by the use of an irreversible thermo-mechanical cohesive zone model. In this model, the degradation of the cohesive strength due to cyclic loading is accounted for through a damage variable for which an evolution equation is given in terms of cohesive zone tractions and displacement jumps. Furthermore, interface failure progressively degrades the heat transfer across the interface. In the model the crack tip singularities for both stress analysis and heat transfer are removed. While the crack growth rates predicted by the simulation results can in principle be described by a Paris law approach, the strength of the proposed model is that the use of global loading parameters is in fact not necessary. Instead, material failure is described through local changes to the coupled mechanical and thermal fields.     

A thermo-mechanical cohesive zone formulation for ductile fracture

The paper addresses the possibility to project both mechanical and thermal phenomena pertinent to the fracture process zone into a cohesive zone. A wider interpretation of the notion cohesive zone is thereby suggested to comprise not only stress degradation due to micro-cracking but also heat generation and energy transport. According to our experience, this widening of the cohesive zone concept allows for a more efficient finite element simulation of ductile fracture. The key feature of the formulation concerns the thermo-mechanical cohesive zone model, evolving within the thermo-hyperelastoplastic continuum, allowing for the concurrent modelling of both heat generation, due to the fracture process, and heat transfer across the fracture process zone. This is accomplished via thermodynamic arguments to obtain the coupled governing equation of motion, energy equation, and constitutive equations. The deformation map is thereby defined in terms of independent continuous and discontinuous portions of the displacement field. In addition, as an extension of the displacement kinematics, to represent the temperature field associated with the discontinuous heat flux across the fracture interface, a matching discontinuous temperature field involving the interface (or band) temperature is proposed. In the first numerical example, concerning dynamic quasi-brittle crack propagation in a thermo-hyperelastoplastic material, we capture the initial increase in temperature close to the crack surface due to the energy dissipating fracture process. In the second example, a novel application of ductile fracture simulation to the process of high velocity (adiabatic) cutting is considered, where some general trends are observed when varying the cutting velocity.     

Steady growth of a crack with a rate and temperature sensitive cohesive zone

The steady-state dynamic propagation of a crack in a heat conducting elastic body is numerically simulated. Specifically, a mode III semi-infinite crack with a nonlinear temperature dependent cohesive zone is assumed to be moving in an unbounded homogeneous linear thermoelastic continuum. The numerical results are obtained via a semi-analytical technique based on complex variables and integral transforms. The relation between the thermo-mechanical properties of the failure zone and the resulting crack growth regime are investigated. The results show that temperature dependent solutions are substantially different from purely mechanical ones in that their existence and stability strongly depends on the cohesive zone thermal properties.     

Bridging effects in cracked laminates under thermal gradients

An approach for the coupled thermomechanical analysis of composite structures with bridged cracks is described. A crack bridging law is presented that accounts for breakdown of load as well as of heat transfer across the crack with increasing crack opening. The crack bridging law is implemented into a finite element framework as a cohesive zone model and is used for the investigation of unidirectional laminates under prescribed temperature gradients. The effects of crack bridging parameters on energy release rates, mode mixity and crack heat flux is discussed for boundary conditions which lead to crack opening either through bending deformation or delamination buckling.     

Simulation of fatigue crack growth at plastically mismatched bi-material interfaces

The present paper reports the results of a study on fatigue crack growth in a system with an interface between two elastic–plastic solids of different yield strength. Fatigue crack growth analysis is conducted by the use of a cohesive zone model. Irreversibility of material separation processes is introduced through the load history dependent degradation of the cohesive strength. Fatigue crack growth is considered to occur along the direction perpendicular to the interface and along the interface. Crack growth rate acceleration, deceleration or arrest, as well as crack bifurcation at the interface are predicted in dependence of the plastic property mismatch of the two solids and the interface properties. The outcome of the simulations is in very good agreement with trends of published experimental data.     

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.     

A thermomechanically coupled viscoelastic cohesive zone model at large deformation

A new viscoelastic cohesive zone model is formulated for large deformation conditions and within a fully coupled thermomechanical framework. The model is suitable for the simulation of a wide range of problems especially for polymeric materials. It can capture viscoelastic crack propagation as well as energy dissipation due to this process. Starting from the principles of thermodynamics, a 3D finite element formulation is derived for a fully coupled simultaneous solution of the thermal field and the deformation field. The viscoelastic model is constructed by extending an elastic exponential traction separation law using a simple rheology. The viscous part of the tractions is postulated to have the same characteristic length as the elastic part and that they are related by a single material parameter. A Newtonian dashpot is used to describe the evolution of the viscous separation. Furthermore, thermal effects are accounted for using temperature expressions in both the traction laws and the viscosity of the dashpot, and using a heat conduction law across the interface. The model is implemented within an implicit finite element code and the internal variable is calculated using an internal iteration. Different numerical examples are used to verify the model and a comparison with experimental data shows a satisfactory agreement.     

NONLINEAR BUCKLING BEHAVIOR OF DAMAGED COMPOSITE SANDWICH PLATES CONSIDERING THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL AND MECHANICAL PROPERTIES

On the basis of the first-order shear deformation plate theory and the zig-zag deformation assumption, an incremental finite element formulation for nonlinear buckling analysis of the composite sandwich plate is deduced and the temperature-dependent thermal and mechanical properties of composite is considered. A finite element method for thermal or thermo-mechanical coupling nonlinear buckling analysis of the composite sandwich plate with an interfacial crack damage between face and core is also developed. Numerical results and discussions concerning some typical examples show that the effects of the variation of the thermal and mechanical properties with temperature, external compressive loading, size of the damage zone and ply angle of the faces on the thermal buckling behavior are significant. Project supported by the National Natural Science Foundation of China (No. 59975013).     

A cohesive zone model for fatigue crack growth allowing for crack retardation

A damage-based cohesive model is developed for simulating crack growth due to fatigue loading. The cohesive model follows a linear damage-dependent traction–separation relation coupled with a damage evolution equation. The rate of damage evolution is characterized by three material parameters corresponding to common features of fatigue behavior captured by the model, namely, damage accumulation, crack retardation and stress threshold. Good agreement is obtained between finite element solutions using the model and fatigue test results for an aluminum alloy under different load ratios and for the overload effect on ductile 316 L steel.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Integrated numerical–experimental analysis of interfacial fatigue fracture in SnAgCu solder joints

In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages.     

Delamination of an elastic film from an elastic–plastic substrate during adhesive contact loading and unloading

Adhesive contact between a rigid sphere and an elastic film on an elastic–perfectly plastic substrate was examined in the context of finite element simulation results. Surface adhesion was modeled by nonlinear springs obeying a force-displacement relationship governed by the Lennard–Jones potential. A bilinear cohesive zone law with prescribed cohesive strength and work of adhesion was used to simulate crack initiation and growth at the film/substrate interface. It is shown that the unloading response consists of five sequential stages: elastic recovery, interface damage (crack) initiation, damage evolution (delamination), film elastic bending, and abrupt surface separation (jump-out), with plastic deformation in the substrate occurring only during damage initiation. Substrate plasticity produces partial closure of the cohesive zone upon full unloading (jump-out), residual tensile stresses at the front of the crack tip, and irreversible downward bending of the elastic film. Finite element simulations illustrate the effects of minimum surface separation (i.e., maximum compressive surface force), work of adhesion and cohesive strength of the film/substrate interface, substrate yield strength, and initial crack size on the evolution of the surface force, residual deflection of the elastic film, film-substrate separation (debonding), crack-tip opening displacement, and contact instabilities (jump-in and jump-out) during a full load–unload cycle. The results of this study provide insight into the interdependence of contact instabilities and interfacial damage (cracking) encountered in layered media during adhesive contact loading and unloading.     

基于统一相场理论的早龄期混凝土化-热-力多场耦合裂缝模拟与抗裂性能预测

受水化反应和热量传输等过程影响, 混凝土在养护阶段会发生受约束收缩变形, 并由此在结构内引发较大的拉应力, 而此时混凝土力学性能往往还处于较低水平, 容易导致建造期混凝土结构即出现裂缝等病害. 这种早龄期混凝土裂缝对核安全壳、桥梁隧道、地下结构、水工或海工结构等重大土木工程和基础设施的全生命周期完整性、耐久性和安全性造成严重影响. 为了准确预测早龄期混凝土抗裂性能并量化裂缝演化对混凝土结构行为的不利影响, 亟需开展化-热-力多场耦合环境下的混凝土裂缝建模与抗裂性能分析研究. 针对这一需求, 本工作在前期提出的固体结构损伤破坏统一相场理论基础上, 考虑开裂过程与水化反应、热量传输等之间的相互影响, 建立裂缝相场演化特征(包括基于强度的裂缝起裂准则、基于能量的裂缝扩展准则和基于变分原理的扩展方向判据等)与混凝土水化度和温度之间的定量联系, 提出混凝土化-热-力多场耦合相场内聚裂缝模型, 发展相应的多场有限元数值实现算法并应用于若干验证算例. 数值模拟结果表明, 上述多场耦合相场内聚裂缝模型合理地考虑了水化反应、热量传输、力学行为以及裂缝演化之间的耦合效应, 揭示了早龄期混凝土热膨胀变形和自收缩变形的相互竞争机理, 且分析结果不受裂缝尺度和网格大小等数值参数的影响, 实现了早龄期裂缝演化全过程准确模拟和抗裂性能定量预测, 有望在混凝土结构早龄期裂缝预测和控制方面发挥重要作用.      

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).     

Experimental investigation of thermal contact conductance for nominally flat metallic contact

A unique experimental set-up was fabricated to carry out axial heat flow steady state experiments for the assessment of thermal contact conductance (TCC) at the interface of two materials. Three different materials (copper, brass and stainless steel) were selected for the experiments considering their mechanical and thermal properties. Heat transfer experiments were performed in vacuum environment (0.045 torr) to find out solid spot contact conductance for nominally flat surfaces with different surface roughness (1–5 μm) for each specimen under several load conditions (0.6–15 MPa). A precise estimation of TCC for the interface of sets of similar materials was one of the most important results of this research. The effects of the surface roughness, the material properties and the load conditions (nominal interface pressure) have been studied and documented. Furthermore, the experimental results of solid spot contact conductance were compared with four theoretical models, showing their limitations to make a precise estimation of the TCC in the range of the used parameters.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

Fracture mechanical assessment of interface cracks with contact zones in piezoelectric bimaterials under thermoelectromechanical loadings: I. Electrically permeable interface cracks

An electrically permeable interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric spaces under the action of a remote electromechanical loading and a temperature flux is considered. Assuming that all fields are independent on the coordinate x₂ co-directed with the crack front, the stresses, the electrical and the temperature fluxes as well as the derivatives of the jumps of the displacements, the electrical potential and the temperature at the interface are presented via a set of analytic functions in the (x₁,x₃)-plane with a cut along the crack. Due to this representation firstly an auxiliary problem concerning the direction of the heat flux permitting a transition from a perfect thermal contact to a separation has been solved for a piezoelectric bimaterial. Besides, an inhomogeneous combined Dirichlet–Riemann boundary value problem has been formulated and solved exactly for the above mentioned interface crack. Stress and electrical displacements intensity factors are found in a clear analytical form which is especially easier for a small contact zone length. A simple equation and a closed form analytical formula for the determination of the real contact zone length have been derived and compared with the associated equation of the classical (oscillating) interface crack model defining the zone of crack faces interpenetration. For a numerical illustration of the obtained results a bimaterial cadmium selenium/glass has been used, and the influence of the heat flux upon the contact zone length and the associated stress intensity factor has been shown.     

On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium

In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t₀ and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t₀, as well as the fiber volume fraction are examined.