Damage accumulation for growth of anti-plane crack in work-hardening material

Elastic–plastic solutions of an anti-plane crack in an infinite body are used in conjunction with a continuum damage model to describe the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to time dependent events. A power law relates the stress to the strain of the material. The damage, which invokes nucleation, growth and coalescence of microvoids due to elevated strain, is confined to the plastic zone surrounding the crack tip. For applied loading below the yield stress, the small-scale and large-scale yielding solutions are used to determine the influence of strain hardening on crack instability and failure. Crack growth due to cyclic loading and time-dependent deformations are studied using the small-scale yielding solution of the deformation theory of plasticity.     

Effect of crack-tip shape on the near-tip field in glassy polymer

The physical nature of a crack tip is not absolutely sharp but blunt with finite curvature. In this paper, the effects of crack-tip shape on the stress and deformation fields ahead of blunted cracks in glassy polymers are numerically investigated under Mode I loading and small scale yielding conditions. An elastic–viscoplastic constitutive model accounting for the strain softening upon yield and then the subsequently strain hardening is adopted and two typical glassy polymers, one with strain hardening and the other with strain softening–rehardening are considered in analysis. It is shown that the profile of crack tip has obvious effect on the near-tip plastic field. The size of near-tip plastic zone reduces with the increase of curvature radius of crack tip, while the plastic strain rate and the stresses near crack tip enhance obviously for two typical polymers. Also, the plastic energy dissipation behavior near cracks with different curvatures is discussed for both materials.     

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic–viscoplastic constitutive relation with various hardening–softening–hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip.On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening(or softening–hardening) has a particularly strong effect on the near crack tip stress and deformation fields.     

A phenomenological model of fatigue crack growth in perfectly plastic infinite plates under completely reversed uniaxial loading

The fatigue failure of a thin infinite center-cracked plate under completely reversed uniaxial loading is considered. A two-stage fatigue crack model including the incubation and crack propagation stages is constructed. The stress distribution in the vicinity of the crack tip is described using the concept of a conventional elastic crack. The crack-tip plastic zone is simulated by a Dugdale thin plastic zone, and the condition for the movement of the failure front is given by criteria of damage mechanics. It is shown that the fatigue crack growth rate in perfectly plastic materials with a plastic zone of constant length is a power-law function of the stress intensity factor range. This relationship is quadratic when the length of the plastic zone is not constant Published in Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 116–127, December 2005.     

Plastic strip model of circular crack under cyclic loading with damage accumulation

A cylindrical solid containing a penny-shaped crack in its mid plane is subjected to a remote tensile stress field. In the plastic region near the crack border, damage due to continuous deterioration of the material accumulates, and may lead to crack instability and crack growth. A damage model relating the crack opening displacement in the plastic zone to the fraction of the cross-sectional area occupied by voids is used to describe the conditions necessary for the onset of crack instability, fatigue crack propagation by cyclic loading, and rates of crack growth for time-dependent environmental effects.     

Fatigue crack growth under anti-plane shear mode deformation

In this paper, the theory of the steady growth of fatigue crack in an infinite medium under the periodic anti-plane remote shear loading has been examined. The criterion of accumulative plastic work for material failure associated with the slip displacement in the fracture process zone of Dugdale type ahead of the crack tip is employed in the analysis. The effect of the locked dislocation in the fracture process zone is considered. Under the assumption that the speed of fatigue crack propagation remains uniform through the fracture process zone, the steady speed of fatigue crack can be expressed as a function of the range of the applied shearing stress and the maximum shearing stress. The effect of the crack size on the fatigue crack speed is discussed. The effect of the finite width of specimen on the speed of fatigue crack speed is investigated. The differences between the present work and the previous studies on fatigue crack speed are discussed.     

过载作用下聚乙烯疲劳裂纹扩展行为研究

论文针对中密度聚乙烯材料(MDPE)，采用平板试样进行了I型疲劳裂纹扩展和单次过载下裂纹扩展试验．发现与金属材料类似，单次拉伸过载对聚乙烯(PE)的疲劳裂纹扩展有明显的迟滞作用，降低了裂纹扩展速率．试验还通过变载荷刻线法获取疲劳裂纹扩展前缘的实际形貌和变化规律，对常规变载荷刻线方法进行了调整和验证，其修正方法对高分子材料的疲劳裂纹扩展前缘刻线具有较好的效果．通过观察发现含楔形塑性区的裂尖钝化是裂纹迟滞的主要原因．过载引入的塑性区内残余应力对裂纹迟滞也起了重要作用．论文利用Dugdale模型计算了塑性区尺寸，使用基于残余应力的Wheeler模型对过载迟滞进行了很好的拟合．     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

Strain and failure analysis of graphite/epoxy plates with cracks

The objective of this investigation was to study the deformation and failure of uniaxially loaded graphite/epoxy plates with cracks and to determine the influence of notch size on failure. The specimens were quasi-isotropic laminates with cracks of various lengths. They were instrumented with strain gages, photoelastic coatings and moiré grids. Strains near the crack tip show two distinct points of rate change at strain levels of 0.002 and 0.006, the latter corresponding to the ultimate strain of the 90-deg plies. Failure near the crack tip takes the form of a damage zone consisting of ply subcracking along fibers, local delamination and fiber breakage. Failure occurs when this damage zone reaches some critical value. Measured maximum strains at failure exceeded twice the ultimate strain of the unnotched laminate. The average stress over a characteristic distance (5 mm) from the crack tip was used as a criterion to describe the influence of crack length on failure. Comparison of results with those from similar specimens with circular holes showed that strength was nearly independent of notch geometry in this case, i.e., specimens with holes and cracks of the same size had nearly the same strength.     

A multiscale model for the ductile fracture of crystalline materials

In this paper, a multiscale model that combines both macroscopic and microscopic analyses is presented for describing the ductile fracture process of crystalline materials. In the macroscopic fracture analysis, the recently developed strain gradient plasticity theory is used to describe the fracture toughness, the shielding effects of plastic deformation on the crack growth, and the crack tip field through the use of an elastic core model. The crack tip field resulting from the macroscopic analysis using the strain gradient plasticity theory displayes the 1/2 singularity of stress within the strain gradient dominated region. In the microscopic fracture analysis, the discrete dislocation theory is used to describe the shielding effects of discrete dislocations on the crack growth. The result of the macroscopic analysis near the crack tip, i.e. a new K-field, is taken as the boundary condition for the microscopic fracture analysis. The equilibrium locations of the discrete dislocations around the crack and the shielding effects of the discrete dislocations on the crack growth at the microscale are calculated. The macroscopic fracture analysis and the microscopic fracture analysis are connected based on the elastic core model. Through a comparison of the shielding effects from plastic deformation and the discrete dislocations, the elastic core size is determined.     

Three-dimensional elastic–plastic finite element analysis for orthogonal cutting with discontinuous chip of 6-4 brass

An elastic–plastic finite element model is developed for 3D orthogonal cutting of discontinuous chips. The tool is P20 while the workpiece is made of 6-4 brass. Examined under the condition of low cutting speed are the initial crack location, the direction of crack growth and variations of discrete chips. These predictions are made possible by application of the strain energy density (SED) theory. The initial crack was formed above the tool tip and grew progressively along the stationary values of the SED function until the trajectory intersects with the free surface. The plastic deformation and friction result in a high equivalent stress in the secondary deformation zone of the first longitudinal chip. Stresses are also high at the location of crack initiation. The chip node near the tool face is sensitive to the contact of the tool face. As more residual stress prevails after the first longitudinal cut, degradation of the workpiece surface prevails and should be accounted for.     

Estimate of the Latent Free Energy and Damage at the Tip of an Opening–Mode Crack

A method of estimating the latent elastic energy associated with the microinhomogeneity of the stress and plastic–strain fields inside the plastic zone localized near the tip of an opening–mode crack (Dugdale zone) under conditions of plane stresses is proposed. The microinhomogeneity of plastic flow upon small strain hardening is taken into account only in the form of considerable distortion of the geometry of the free surfaces of the plastic zone. The damage that developes because of release of the latent free energy is estimated depending on the magnitude of the crack opening.     

Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

Numerical analysis of fatigue striations

A computational model was developed to numerically analyse fatigue striations. The inclined strip yield model with continuous distributions of infinitesimal dislocations was utilized to express the crack tip plasticity in this model. The fatigue crack tip blunting process was approximated by sequential activation of two slip lines under loading, and crack closure during unloading was taken into account. The plastic zone at a growing fatigue crack tip at the maximum load was independent of the crack growth up to ten cycles while the reversed plastic zone decreased in a size to one twentieth of that at the maximum load as the crack grew. The ratio of these plastic zone sizes and also the crack tip opening displacement were quite different from the simple prediction by J.R. Rice for a stationary crack. The computed striation spacings were compared with the observed ones and moderate agreement between them obtained.     

Fatigue fracture model for thin isotropic plates with cracks in axial loading

Conclusion We have constructed a model of the growth of a fatigue crack in a thin, isotropic plate, taking the two-stage evolution of the fracture process into account. The model is based on concepts of the mechanics of a continuous defective state and on a schematic representation of the neighborhood of the tip of a fatigue crack as a plastic zone moving together with the crack. The model takes into account the influence of the cumulative defective state (damage level) along the crack propagation front on the speed of propagation.We have formulated solutions for the cases when the length of the plastic zone is constant and when it varies during the growth of fatigue cracks. We have established the fact that the plastic zone at the crack tip tends to disrupt the stability of the motion immediately at the time of inception or opening of the crack. The speed of crack propagation decreases as the plastic zone grows in size.We have shown that the problem of estimating the kinetics of fatigue cracks in thin plates can be reduced to calculating the growth rate as a function of the peak-to-peak amplitude of the stress intensity factor while preserving the structure of the governing equations of the model. We have also shown that the concept of a plastic zone of constant length induces a power-law dependence of the crack rate on K, the power exponent varying from 2 to 10–12. The Dugdale model gives a square-law dependence of the crack rate on K, which for the most part is applicable to plastic materials.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 7, pp. 53–63, July, 1994.     

Modeling of fatigue crack growth from a notch

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic–plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different R-ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch.     

拉压循环载荷下正交异性钢桥面板肋-面板焊缝裂纹扩展分析

采用四步法计算了考虑循环载荷中压应力影响的正交异性钢桥面板的肋-面板焊缝表面裂纹扩展。第一步是基于正交异性钢桥面板的疲劳分析模型,计算肋-面板焊缝处的应力,第二步是通过肋-面板焊缝的三维局部模型,用Schwartz-Neumann交替法计算焊缝表面裂纹的应力强度因子分布,第三步是用二维断裂力学模型和增量塑性损伤模型,计算循环载荷中的压应力对裂纹扩展的影响,第四步是用第二步中的三维裂纹分析结果和第三步中的二维断裂力学模型得到的裂纹扩展公式,计算钢桥面板的肋-面板焊缝表面裂纹扩展。计算结果表明,对应于正交异性钢桥面板肋-面板焊缝处的循环应力,本文所用模型的裂纹尖端反向塑性区导致裂纹扩展率增加50%以上。研究结果为正交异性钢桥面板肋-面板焊缝裂纹的疲劳寿命分析提供了研究基础。     

三点弯曲试样动态应力强度因子计算研究

利用Hopkinson压杆对三点弯曲试样进行冲击加载,采集了垂直裂纹面距裂尖2mm和与裂纹面成60°距裂尖5mm处的应变信号。根据裂尖附近测试的应变信号计算试样的动态应力强度因子,并与有限元计算结果进行比较,结果表明由于裂尖有一段疲劳裂纹区,通过裂尖附近应变信号来计算动态应力强度因子时,如果裂尖位置确定不准及粘贴应变片位置不够准确对计算结果将带来很大影响。因此利用应变片法计算动态应力强度因子时,为了获得更准确的计算结果,在实验后应对试件裂纹面进行分析测量,重新确定裂尖位置,必要时需对应变片至裂尖距离进行修正后再计算动态应力强度因子值。     

随机载荷下疲劳裂纹的闭合和扩展估算模型

本文分析了裂尖前,后方塑性区对闭合性能的影响,提出从裂尖塑性钝化量和尾迹区残余塑性变形两个方面来确定裂纹面的残余变形,并讨论了压缩载荷对闭合应力的影响,由此建立了一个疲劳裂纹闭合模型,然后通过模型“有限记忆”性质的假定将它应用到随机加载情况。用此模型对铝合金2219——T851受飞机谱载荷的CCT平面应力试件进行了疲劳寿命估算,估算值与实验结果接近。     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China