Simulation of lattice orientation effects on void growth and coalescence by crystal plasticity

A three dimensional rate-dependent crystal plasticity model is applied to study the influence of crystal orientation and grain boundary on the void growth and coalescence. The 3D computational model is a unit cell including one sphere void or two sphere voids. The results of three different orientations for single crystal and bicrystals are compared. It is found that crystallographic orientation has noticeable influences on the void growth directionvoid shape, and void coalescence of single crystal. The void growth rate of bicrystals depends on the crystallographic orientations and grain boundary direction.

SURFACE EFFECT ON NANOSIZED VOID GROWTH IN A RIGID-PERFECTLY PLASTIC MATERIAL

The influence of the surface effect on the nanosized spherical void growth in a rigidperfectly plastic material is analyzed and the mechanism of the nanosized void growth with high triaxiality is given. Based on the Rice and Tracey model for a macro void growth, the present model is proposed to account for the nanosized void growth under a uniform remote strain rate field with consideration on the surface effect. It is concluded that the surface effect yields an evident resistant influence on the nanosized void growth. That is, this influence decays as the void radius increases. With high triaxiality, the nanosized void growth is divided into two stages： the initial stage and the mature stage. At the first stage, the void grows slowly and the influence of surface effect is relatively weak, whereas at the second stage, the influence is significant and the void grows drastically.

CONSTITUTIVE POTENTIAL FOR DUCTILE DAMAGED MATERIAL AND VOID GROWTH RATE

In this paper a general formula for plastic potential including isotropic ductile damage has been present ed on the basis of the thermodynamics for irreversible process and internal variable the- ory.With this formula the mass conservation law is satisfied and it also contains a series of unknow coefficients which are the function of macro equivalent stress and the average micro equivalent stress and an unknown function which is the function of two generalized forces. The approximate yield surface equation for isotropically damaged materials is developed.Using this equation the void growth rate is calculated for nonlinear material containing voids.The present re- sults are in good agreement with the numerical results given by the cell model.

THE EFFECT OF STRAINING MODE ON VOID GROWTH

Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results.

Factors Affecting the Relation of Fracture Toughness V_(GC) with Critical Void Growth Ratio R_C/R_O

The relationship between fracture toughness VGC and critical void growth RC/RO was studied for ten kinds of Steel. The macroscopic fracture toughness VGC was determined by using notched tensile specimens. and the microscopic parameters of critical void growth ratio RC/RO were quantitatively measured under SEM. Then, the coefhcient C in the relation VGC = C In(RC/RO) proposed in author's past work was specifically explored. The correlation of C with tensile proderty parameter φ=σyδ/(Eφn) was presented for the Steel investigated, and the effects of low temperature on C were also discussed. Results show that the coefficient C is linearly related to the parameter and insensitive to low temperature.

Void Growth and Interaction in a Structural Aluminum Alloy: Experiments and Theory

The problem of void growth and interaction is of importance to understanding the mechanics of failure in metals exhibiting ductility. In this work, the growth and interaction of voids in 6061-T6 aluminum were studied experimentally. Specifically, holes of varying numbers and relative placement were investigated for their normalized area growth with applied displacement. Flat dog-bone specimens were carefully drilled in their gauge area with no (zero) holes, one hole, and two holes (arranged vertically or horizontally) for experimentation after polishing. The growth of holes, captured by video recordings, exhibited exponential behavior and was influenced greatly by the number and arrangement of holes with the horizontal voids growing the fastest and the vertical ones growing the slowest. Also, the ensuring deformation of the sample was studied using load-displacement curves, pictography and videography, SEM imaging and Atomic Force Microscopy (AFM). The methods revealed that although the major part failure is due to large crack formation, it was preceded by intense dislocation slip activity and the formation of micro cavities. Also, the AFM quantified the three-dimensional nature of crystal or grain deformation and how it is greatly influenced by distance and location from the hole. Lastly, theoretical understanding of hole growth was offered.

Molecular dynamics study on the nano-void growth and coalescence at grain boundary

Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjected to uniaxial tension strain with one-void and two-void at the centered grain boundary were employed to analyze the effect of specimen size, temperature and applied strain rate on the stress-strain response, incipient yield strength and macroscopic effective Young's modulus. The evolutions of dislocations, twin bands and void shapes under different specimen sizes were also presented. The obtained results show that, regardless of the void numbers, the specimen sizes, temperature, the applied strain rate had significant influence on the void shape evolution, stress-strain curve and incipient yield strength, while negligible effects on the macroscopic effective Young's modulus except for the temperature. Moreover, the voids growth rate along the grain boundary was also found to be associated with the specimen sizes.

Void Formation and Growth for a Class of Compressible Hyper-Elastic Sphere

In this paper, the strain energy function proposed by Shang and Cheng was generalized by introducing a nonlinear term. Void formation and growth in the interior of a sphere composed of compressible hyper-elastic material, subjected to a prescribed uniform displacement, was examined. A parametric cavitated bifurcation solution for the radial deformed function was obtained. Stability of the solution of the cavitated bifurcation equation was discussed. With the appearance of a cavity, an interesting feature of the radial deformation near the deformed cavity wall is the transition from extension to compression.

Growth of a Void in a Rubber Rectangular Plate under Uniaxial Extension

The finite deformation and stress analyses for a rectangular plate with a center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper. An approximation solution was obtained from the minimum potential energy principle. The numerical results for the growth of the cavitation and stresses along the edge of the cavitation were discussed. In addition, the stress concentration phenomenon was considered.

A New Void Growth Model for Dynamically Loaded Ductile Materials~*

In this paper, a new model to describe the dynamic ductile fracture is proposed. The constitutive relation of the elastic-viscoplastic matrix has an overstress form given by previous authors. A dynamic loading surface at constant equivalent strain rate(with the volumetric part also taken into account) is derived and an approximate expression for this dynamic loading surface is suggested. In the case where the porous material element is subjected to spherically symmetric tension, the Carroll-Holt’s model and Johnson’s model are recovered; and in the case where the strain rate sensitivity of the material tends to zero, the Gurson’s model is recovered. Moreover, the normality condition of the plastic strain rate for the dynamic loading surface is discussed, and it is shown that the normality rule is no longer valid in general. Finally, comparisons of this model with the models recently proposed by Pan, Saje and Needleman as well as by Perzyna are also presented.

THE GROWTH OF THE VOID IN A HYPERELASTIC RECTANOULAR PLATE UNDERA UNIAXIAL EXTENSION

In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelusticannular plate and its approximate solution is obtained from the minimum potentialenergy principle. The growth of the cavitation iS also nunterically computed andanalysed.

Growth of Voids in a Hyperelastic Rectangular Plate

The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.

Influence of crystallographic orientation on growth behavior of spherical voids

The influence of crystallographic orientation on the void growth in FCC crystals was numerically simulated with 3D crystal plasticity finite element by using a 3D unit cell including a spherical void,and the rate-dependent crystal plasticity theory was implemented as a user material subroutine.The results of the simulations show that crystallographic orientation has significant influence on the growth behavior of the void.Different active slip systems of the regions around the void cause the discontinuity in lattice rotation around the void,and the corner-like region is formed.In the case of the void located at grain boundary,large heterogeneous deformation occurs between the two grains,and the equivalent plastic deformation along grain boundary near the void in the case of θ=45°(θ is the angle between grain boundary direction and X-axis) is larger than the others.Large difference of orientation factor of the two grains leads to large equivalent plastic deformation along grain boundary,and the unit cell is more likely to fail by intergranular fracture.

TRANSVERSELY ISOTROPIC HYPER-ELASTIC MATERIAL RECTANGULAR PLATE WITH VOIDS UNDER A UNIAXIAL EXTENSION

The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared.

Assessment of a two-surface plasticity model for hexagonal materials

A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution(rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.

基于孔洞长大理论的多轴蠕变设计模型及其工程应用

多轴蠕变是高温构件失效的重要原因,工程设计中必须予以考虑。本文介绍了以孔洞长大理论为基础的多轴蠕变设计方法;探讨了孔洞长大的基本原理;讨论了基于该理论的5个常用模型;分析了这些模型在R5、ASME III、RCC-MR及VGB-R 509L中的应用,指出了高温构件多轴蠕变设计的困难,并对进一步的工作提出了建议。

金属塑性材料细观损伤过程声发射特性实验研究

采用声发射基本参数能量计数对金属塑性材料细观损伤机制及微孔洞演化过程进行研究。以20钢和Q345钢为例,采用GTN模型模拟求得光滑缺口试件拉伸过程中细观损伤参数的变化情况,进行拉伸实验获取材料的力学及声发射信息。结合模拟和实验数据,分析两种试件拉伸过程孔洞扩张比和累积能量计数的变化规律,建立基于累积能量计数的孔洞扩张比量化评价经验公式。结果表明:采用累积能量计数解释金属塑性材料的微孔洞演化过程清晰合理,可以有效区分20钢与Q345钢的细观损伤差异。

基于GTN模型的20钢孔洞扩张比数值模拟

孔洞扩张比VG可以作为描述钢材损伤时微孔洞演化情况的细观损伤变量,GTN模型可用于金属塑性材料的细观损伤有限元模拟。应用GTN模型模拟20钢圆棒型缺口试件拉伸过程的不同阶段,得到细观损伤参量应力三轴度Rσ、等效塑性应变εp、孔洞体积百分数f及孔洞扩张比VG在试件中心截面的变化规律。结果表明:在整个拉伸过程中,上述参数的数值随着载荷的增加而增大,且εp对VG的影响较大。当试件断裂时,试件缺口截面中心位置的细观损伤参量值大于缺口根部的值,此时20钢的临界孔洞扩张比VGC为3.134。

绝热剪切带内微孔洞演化规律研究

为深入了解绝热剪切带内微孔洞的演化规律 ,进而揭示高应变率加载条件下绝热剪切破坏的特殊规律 ,本文对D35钢进行了约束爆破实验 ,爆破后回收圆筒的微观观察表明 ,绝热剪切破坏要经过绝热剪切带内微孔洞形核、长大和相互联接形成裂纹等一系列演化过程。在GuduruP等人的测试结果和LiShaofan等人数值仿真结果基础上 ,通过简化 (剪切带内的温度分布为由剪切带中心向边缘线性降低 ,并最终降至与基体温度相同 ;微孔洞的形核、长大受温度控制 ,长大速度随温度呈指数规律降低 )对TimothySP和HutchingsIM的模型进行了修正 ,修正后的模型可以定量的描述绝热剪切带内微孔洞的演化直至破坏的全过程 。

层裂损伤孔洞增长模型参数的确定方法及其应用

基于自由面速度曲线及其与层裂面处物理量变化之间的关联,考虑层裂损伤演化过程中波的传播与相互作用,进一步探讨了损伤演化过程中的临界状态,分析了孔洞增长层裂损伤模型参数所包含的物理涵义,并给出基于物理的模型参数确定方法.通过对两种典型延性金属OFHC铜和钽层裂实验结果的模拟,验证了该方法的合理性.本文给出的参数确定方法不仅可以扩展模型的适用范围,有效提高计算结果的可信度,同时,也为其他层裂损伤模型参数的确定提供了很好的借鉴作用.