Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

Dynamic deformation and failure mechanisms in polycrystalline ceramics are investigated through constitutive modeling and numerical simulation. Two ceramics are studied: silicon carbide (SiC, hexagonal crystal structure) and aluminum oxynitride (AlON, cubic crystal structure). Three dimensional finite element simulations incorporate nonlinear anisotropic elasticity for behavior of single crystals within polycrystalline aggregates, cohesive zone models for intergranular fracture, and contact interactions among fractured interfaces. Boundary conditions considered include uniaxial strain compression, uniaxial stress compression, and shear with varying confinement, all at high loading rates. Results for both materials demonstrate shear-induced dilatation and increasing shear strength with increasing confining pressure. Failure statistics for unconfined loading exhibit a smaller Weibull modulus (corresponding to greater scatter in peak failure strength) in AlON than in SiC, likely a result of lower prescribed cohesive fracture strength and greater elastic anisotropy in the former. In both materials, the predicted Weibull modulus tends to decrease with an increasing number of grains contained in the simulated microstructure.     

Models of multiaxial fatigue fracture and service life estimation of structural elements

We study criteria and models of multiaxial fracture under the conditions of low-cycle fatigue (LCF). The model parameters are determined by using the data of uniaxial fatigue tests for different coefficients of the cycle asymmetry. A procedure for calculating the stress state of the compressor disk in a gas turbine engine (GTE) in the flight cycle of loading is outlined. The calculated stress state and models of multiaxial fatigue fracture are used to estimate the service life of the compressor disk. The results are compared with the observational data collected during the operation.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

Law of damage accumulation and fracture criteria in highly filled polymer materials

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2–3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account.     

Mechanics and physics of energy density theory

As a departure from the classical continuum mechanics approach, irreversible material behavior is uniquely identified with the exchange of surface and volume energy density through the rate of change of volume with surface area. This provides an one-to-one correspondence between the uniaxial and multiaxial stress or energy state. Equivalent uniaxial stress and strain response can thus be determined for each material element that undergoes damage by permanent deformation and/or fracture. Discussed in detail are the applications of surface energy or volume energy with continuum mechanics theories for analyzing failure in contrast to the strain energy density that analyzes stress and failure simultaneously. In particular, the results for the progressive damage of a slowly moving crack are presented and compared with those obtained from the theory of plasticity. It is shown that the neglected of dilatational energy in plasticity results in inaccurate prediction of the state of affairs near the crack tip.Since the stresses and strains in the strain energy density theory are determined separately, nonlinear and finite strains may be easily included into dV/dA and incorporated into the formulation. This opens the door to a class of nonlinear problems that can be solved directly even for finite and large strains including energy dissipation.     

Strain strengthening effects in Witwatersrand quartzite

A series of uniaxial compression specimens were tested over a range of applied ram displacement rates of 8.9 × 10⁻⁴ to 8.9 mm/sec to elucidate the effects of loading rate on the uniaxial compressive fracture stress of Witwatersrand quartzite. It was demonstrated that even within standard loading rate ranges, considerable scatter in the fracture strength (under uniaxial compression) existed in this particular quartzite rock. Nevertheless, a definite trend of increasing fracture resistance with increasing monotonic loading rate was evident inasmuch that increasing the loading rate (strain rate) by four orders of magnitude increase the fracture strength by almost 2.8 times. Prior fatigue loading also produced a significant strain strengthening as the uniaxial compressive fracture stress tended to increase in a sigmoidal fashion with increasing number of fatigue cycles prior to testing. Indeed, the fracture strength of quartzite was almost doubled in value after 10⁻ cycles. Plane strain fracture toughness tests utilising three point bend specimens were conducted and an average of K_lc = 1.7 MPa√m was realized. In both the uniaxial compression tests and the fracture toughness tests, failure occurred by crack extension predominantly by a transgranular flat cleavage-like mode through pure quartzite (silica) regions. However, crack extension was also observed to occur in an intergranular “ductile-like” mode through areas associated with inclusions prevalent in the quartzite.     

半结晶聚合物损伤演化的实验表征与数值模拟

损伤本构模型对研究材料的断裂失效行为有重要意义, 但聚合物材料损伤演化的定量表征实验研究相对匮乏. 通过4种高密度聚乙烯(high density polythylene, HDPE)缺口圆棒试样的单轴拉伸实验获得了各类试样的载荷-位移曲线和真应力-应变曲线, 采用实验和有限元模拟相结合的方法确定了HDPE材料不同应力状态下的本构关系, 并建立了缺口半径与应力三轴度之间的关系;采用两阶段实验法定量描述了4种HDPE试样单轴拉伸过程中的弹性模量变化, 并建立了基于弹性模量衰减的损伤演化方程, 结合中断实验和扫描电子显微镜分析了应力状态对HDPE材料微观结构演化的影响. 结果表明缺口半径越小, 应力三轴度越大, 损伤起始越早、演化越快; 微观表现为: 高应力三轴度促进孔洞的萌生和发展, 但抑制纤维状结构的产生;基于实验和有限元模拟获得的断裂应变、应力三轴度、损伤演化方程等信息提出了一种适用于聚合物的损伤模型参数确定方法, 最后将本文获得的本构关系和损伤模型用于HDPE平板的冲压成形模拟, 模拟结果与实验结果吻合良好.      

A study of crack-tip nonlinearities in frozen-stress fields

A mechanical and optical characterization study in a uniaxial field was conducted on a commercial di-phase photoelastic material suitable for stress freezing. Results were used in a plane-strain theory for predicting nonlinear crack-tip behavior with the Prandtl-Reuss equations and a Mises criterion. These predictions were compared with frozen-stress photoelastic results obtained from experiments on a variety of technologically important three-dimensional cracked-body problems. Results indicate substantially greater stiffness or constraint in the nonlinear zone near the crack tip than predicted using uniaxial data. However, the value of the maximum shear stress at the onset of nonlinear behavior was accurately established and was the same for all cases examined.     

柔性硅泡沫薄片的短时松弛行为研究

根据多孔硅泡沫材料的单轴压缩和应力松弛实验,利用最小二乘法的LM法拟合得到硅泡沫材料的本构关系.基于上述模型开展了组合结构中多孔泡沫薄片应力松弛行为的数值模拟,得到了短时松弛过程中硅泡沫结构件的应力变化规律.     

Size dependent response of large shell elements under in-plane tensile loading

Large-scale thin-walled structures with a low weight-to-stiffness ratio provide the means for cost and energy efficiency in structural design. However, the design of such structures for crash and impact resistance requires reliable FE simulations. Large shell elements are used in those simulations. Simulations require the knowledge of the true stress–strain response of the material until fracture initiation. Because of the size effects, local material relation determined with experiments is not applicable to large shell elements. Therefore, a numerical method is outlined to determine the effect of element size on the macroscopic response of large structural shell elements until fracture initiation. Macroscopic response is determined by introducing averaging unit into the numerical model over which volume averaged equivalent stress and plastic strain are evaluated. Three different stress states are considered in this investigation: uniaxial, plane strain and equi-biaxial tension. The results demonstrate that fracture strain is highly sensitive to size effects in uniaxial tension whereas in plane strain or equi-biaxial tension size effects are much weaker. In uniaxial and plane strain tension the fracture strain for large shell elements approaches the Swift diffuse necking condition.     

Time-dependent behavior of passive skeletal muscle

An isotropic three-dimensional nonlinear viscoelastic model is developed to simulate the time-dependent behavior of passive skeletal muscle. The development of the model is stimulated by experimental data that characterize the response during simple uniaxial stress cyclic loading and unloading. Of particular interest is the rate-dependent response, the recovery of muscle properties from the preconditioned to the unconditioned state and stress relaxation at constant stretch during loading and unloading. The model considers the material to be a composite of a nonlinear hyperelastic component in parallel with a nonlinear dissipative component. The strain energy and the corresponding stress measures are separated additively into hyperelastic and dissipative parts. In contrast to standard nonlinear inelastic models, here the dissipative component is modeled using an evolution equation that combines rate-independent and rate-dependent responses smoothly with no finite elastic range. Large deformation evolution equations for the distortional deformations in the elastic and in the dissipative component are presented. A robust, strongly objective numerical integration algorithm is used to model rate-dependent and rate-independent inelastic responses. The constitutive formulation is specialized to simulate the experimental data. The nonlinear viscoelastic model accurately represents the time-dependent passive response of skeletal muscle.     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part I. Flour dough

Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension.     

Photovisco-elastoplastic behavior of polycarbonate material under creep and tension tests

Polymers are widely used as photomechanical models of a prototype material (often a metal). Photoplasticity is one of the methods used in order to show the behavior of plastic materials stressed beyond the linear elastic limit. To illustrate this process we have analyzed the photovisco-elastoplastic behavior of polycarbonate as a photoplastic material. In this paper a technique for local and simultaneous measurement of birefringence and principal strains is presented. The mechanical and optical properties, at room temperature, have been evaluated by means of uniaxial tension tests. A series of creep tests has been carried out in order to study the photovisco-elastoplastic behavior of polycarbonate. In two different experiments we analyzed nonlinear birefringence and the amplitude of the corresponding strains. We could thus evaluate the distribution of strains and the distribution of uniaxial stress for each birefringence state and vice versa.     

基于颗粒离散元法的连接键应变软化模型及其应用

基于颗粒间的有限接触假设,提出了可表述颗粒间力、力矩传递的连接键模型. 为了表征连接键的塑性、损伤及断裂过程,在连接键中引入了考虑应变软化效应的Mohr-Coulomb 准则及最大拉应力准则. 单一连接键的单向拉伸测试及直剪测试表明了上述连接键应变软化模型的计算精度. 研究了颗粒体系的宏观应变能与颗粒平均配位数的对应关系. 通过计算发现,对于二维颗粒体系,当平均配位数为5 时,颗粒体系的宏观应变能与相同参数下连续介质方法(如有限元等) 计算获得的应变能基本一致. 利用上述连接键应变软化模型对岩石的单轴压缩过程进行了模拟,计算结果表明:岩石单轴压缩的应力应变曲线经历了线性上升段、非线性上升段、非线性下降段及缓变段等4 个阶段,并给出了上述4 个阶段与岩石内部损伤破裂状态的内在联系. 计算结果还表明,随着断裂应变的增大,岩石的破裂模式逐渐由拉剪复合型破裂向单一压剪型破裂转化;随着断裂应变的增大,峰值应力及达到峰值应力时的应变均逐渐增大,但峰值时的破裂度及终态时的破裂度将逐渐减小.      

Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression

Based on experimental results of brittle, intact sandstone under uniaxial compression, the micro-parameters were firstly confirmed by adopting particle flow code(PFC2D). Then, the validation of the simulated models were cross checked with the experimental results of brittle sandstone containing three parallel fissures under uniaxial compression. The simulated results agreed very well with the experimental results, including the peak strength, peak axial strain, and ultimate failure mode. Using the same microparameters, the numerical models containing a new geometry of three fissures are constructed to investigate the fissure angle on the fracture mechanical behavior of brittle sandstone under uniaxial compression. The strength and deformation parameters of brittle sandstone containing new three fissures are dependent to the fissure angle. With the increase of the fissure angle, the elastic modulus, the crack damage threshold,and the peak strength of brittle sandstone containing three fissures firstly increase and secondly decrease. But the peak axial strain is nonlinearly related to the fissure angle. In the entire process of deformation, the crack initiation and propagation behavior of brittle sandstone containing three fissures under uniaxial compression are investigated with respect tothe fissure angle. Six different crack coalescence modes are identified for brittle sandstone containing three fissures under uniaxial compression. The influence of the fissure angle on the length of crack propagation and crack coalescence stress is evaluated. These investigated conclusions are very important for ensuring the stability and safety of rock engineering with intermittent structures.     

Tensile failure of two-dimensional quasi-brittle foams

Stress redistribution caused by damage onset and the subsequent local softening plays an important role in determining the ultimate tensile strength of a cellular structure. The formation of damage process zones with struts dissipating a finite amount of fracture energy will require the macroscopic stress to be increased in order to continue structural damage. The goal of this paper is to investigate the influence of the fracture energy of the solid on the tensile fracture strength and the strain to fracture in quasi-brittle two-dimensional foams using a microstructural model. We analyze the mesoscopic damage and failure mechanisms in uniaxial tension. Relative density, strut cross-sectional profile, solid’s fracture strain, and fracture energy are varied systematically. The effect of the specific fracture energy on the peak behavior has been shown to be captured by the ratio of the fracture energy to the stored elastic energy. We have also explored the net section strength variation in the presence of a central crack at two different fracture energies. Comparison is made between two structurally identical quasi-brittle and ductile strain hardening foams to identify the differences in the damage mechanisms.     

Empirical plasticity models applied for paper sheets having different anisotropy and dry solids content levels

The rheological nature of paper or board is usually treated either as elasto-plastic or as viscoelastic depending on the studied paper making process or behavior in converting and end use. In this paper we study several stress–strain curve models and the determination of material parameters from an elasto-plastic point of view. Finally, a suitable approach for all stress–strain curves measured from 180 strips is constructed using a linear function for an elastic region and a nonlinear function for a strain hardening region. This model determines a proportional limit (elastic limit) and gives fairly elegant dependencies between material/fitting parameters and two important factors of mechanical properties of paper: dry solids content and anisotropy. In this paper the dependency of a plastic strain on dry solids content and anisotropy is estimated using the introduced stress–strain curve model. Correspondingly, the model can be used to estimate many other mechanical behaviors, for example, the tension differences arising from non-uniform moisture content of the paper web profile. However, the main target of this study is to produce competent parameters based on modeled stress–strain curves for further construction of a material model. This elasto-plastic material model will be utilized in out-of-plane deformation and fracture models.     

A thermo-viscoelastic–viscoplastic–viscodamage constitutive model for asphaltic materials

A temperature-dependent viscodamage model is proposed and coupled to the temperature-dependent Schapery’s nonlinear viscoelasticity and the temperature-dependent Perzyna’s viscoplasticity constitutive model presented in Abu Al-Rub et al., 2009, Huang et al., in press in order to model the nonlinear constitutive behavior of asphalt mixes. The thermo-viscodamage model is formulated to be a function of temperature, total effective strain, and the damage driving force which is expressed in terms of the stress invariants of the effective stress in the undamaged configuration. This expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth. A systematic procedure for obtaining the thermo-viscodamage model parameters using creep test data at different stress levels and different temperatures is presented. The recursive-iterative and radial return algorithms are used for the numerical implementation of the nonlinear viscoelasticity and viscoplasticity models, respectively, whereas the viscodamage model is implemented using the effective (undamaged) configuration concept. Numerical algorithms are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The model is then calibrated and verified by comparing the model predictions with experimental data that include creep-recovery, creep, and uniaxial constant strain rate tests over a range of temperatures, stress levels, and strain rates. It is shown that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions.     

Growth of an arc-crack in bonded dissimilar materials

The problem of growth of a crack lying along the interface of a circular inclusion embedded in an infinite plate is studied within the framework of linear elasticity. The plate is subjected to a uniform uniaxial stress at infinity at any angle of inclination relatively to the crack. The critical load for unstable crack growth, the angle of initial crack extension and the subsequent crack path are investigated using the strain energy density fracture criterion. The combined effect of crack length and orientation on the fracture stress is considered for the case of an aluminum-epoxy composite.