On the determination of the cohesive zone parameters for the modeling of micro-ductile crack growth in thick specimens

The paper deals with the determination of the cohesive zone parameters (separation energy, , and cohesive strength, T _max) for the 3D finite element modeling of the micro-ductile crack growth in thick, smooth-sided compact tension specimens made of a low-strength steel. Since the cohesive zone parameters depend, in general, on the local constraint conditions around the crack tip, their values will vary along the crack front and with crack extension. The experimental determination of the separation energy via automated fracture surface analysis is not accurate enough. The basic idea is, therefore, to estimate the cohesive zone parameters, and T _max, by fitting the simulated distribution of the local crack extension values along the crack front to the experimental data of a multi-specimen J _IC-test. Furthermore, the influence of the cohesive zone parameters on the crack growth behavior is investigated. The point of crack growth initiation is determined only by the magnitude of . Both and T _max affect the crack growth rate (or the crack growth resistance), but the influence of the cohesive strength is much stronger than that of the separation energy. It turns out that T _max as well as vary along the crack front. In the center of the specimen, where plane strain conditions prevail, the separation energy is lower and the cohesive strength is higher than at the side-surface.     

Stress Intensity Factor and Plastic Zone of Auxetic Materials: A Fracture Mechanics Approach to a Chiral Structure Having Negative Poisson’s Ratio

This article summarizes the method of analytical formulation and computational approach of stress intensity factor and plastic zone calculation for auxetic materials, which have negative Poisson’s ratio. A chiral structure-based material is selected as an object of the study due to its popularity. The stress intensity factor is used in combination with the von Mises yielding condition to estimate the plastic zone’s shape and size. The results show that macroscopically the shape of the plastic zone for auxetic material is the same with that of ordinary materials. However, its size is smaller due to the reduction in its Young’s modulus from the solid material of which the auxetic material is made. Microscopically, an auxetic material has its plastic zone shape that is unique to its microstructure. Homogenization theory was convenient to use to bridge between the microscopic and macroscopic models.     

Fracture toughness behavior in the ductile-brittle transition region of the tempered martensitic Eurofer97 steel: Experiments and modeling

The fracture toughness of the tempered martensitic stainless steel Eurofer97 has been experimentally characterized in the ductile-to-brittle transition (DBT) region with sub-sized compact tension specimens. The median fracture toughness-temperature curve in the lower transition region has been found to deviate somewhat from the master curve as described in the ASTM E1921-03 standard. Two-dimensional finite element simulations of the compact tension specimen have been performed. The analysis of the stress fields around the crack tip have been used to define a local criterion for cleavage based upon the attainment of a critical stress over a critical area. This local criterion has been used to reconstruct the lower bound in the transition region. The calibration procedure of the critical parameters has been discussed in detail as well as the uncertainty in the critical values. It is shown in particular that the critical stress is well defined while the model leads to a rather larger uncertainty in the determination of the critical area.     

A reappraisal of transition elements in linear elastic fracture mechanics

This article offers a detailed comparison of the transition elements described by P.P. Lynn and A.R. Ingraffea [International Journal for Numerical Methods in Engineering 12,1031–1036] and C. Manu[Engineering Fracture Mechanics 24,509–512]. The source of a numerical phenomenon in using Manu's transitionelement (TE) is explained. The effect of eight-noded TEs with differentquarter-point elements (QPE) on the calculated stress intensity factors (SIFs) isinvestigated. Strain at the crack tip is shown to be singular for any ray emanating from the crack tip within an eight-noded TE, but strain has bothr ^–1/2andr ^–1singularities, withr ^–1/2dominating for large TEs. Semi-transition elements (STEs) are defined and shown to have a marginal effect on the calculated SIFs. Nine-nodedtransition elements are formulated whose strain singularity is shown to be the same as that of eight-noded TEs. Then the effect of eight-noded and nine-noded TEs with collapsed triangular QPEs, and rectangular and nonrectangular quadrilateral eight-noded and nine-noded QPEs, is studied, and nine-noded TEs are shown to behave exactly like eight-noded TEs with rectangular eight-noded and nine-noded QPEs and to behave almost the same with other QPEs. The layered transition elements proposed by V. Murti and S.Valliapan [Engineering Fracture Mechanics 25, 237–258] areformulated correctly. The effect of layered transition elements is shown by two numerical examples.     

Multiscale prediction of mechanical behavior of ferrite–pearlite steel with numerical material testing

Multiscale mechanical behaviors of ferrite–pearlite steel were predicted using numerical material testing (NMT) based on the finite element method. The microstructure of ferrite–pearlite steel is regarded as a two‐component aggregate of ferrite crystal grains and pearlite colonies. In NMT, the macroscopic stress–strain curve and the deformation state of the microstructure were examined by means of a two‐scale finite element analysis method based on the framework of the mathematical homogenization theory. The microstructure of ferrite–pearlite steel was modeled with finite elements, and constitutive models for ferrite crystal grains and pearlite colonies were prepared to describe their anisotropic mechanical behavior at the microscale level. While the anisotropic linear elasticity and the single crystal plasticity based on representative characteristic length have been employed for the ferrite crystal grains, the constitutive model of a pearlite colony was newly developed in this study. For that reason, the constitutive behavior of the pearlite colony was investigated using NMT on a smaller scale than the scale of the ferrite–pearlite microstructure, with the microstructure of the pearlite colony modeled as a lamellar structure of ferrite and cementite phases with finite elements. On the basis of the numerical results, the anisotropic constitutive model of the pearlite colony was formulated based on the normal vector of the lamella. The components of the anisotropic elasticity were estimated with NMT based on the finite element method, where the elasticity of the cementite phase was numerically evaluated with a first‐principles calculation. Also, an anisotropic plastic constitutive model for the pearlite colony was formulated with two‐surface plasticity consisting of yield functions for the interlamellar shear mode and yielding of the overall lamellar structure. After addressing the microscopic modeling of ferrite–pearlite steel, NMT was performed with the finite element models of the ferrite–pearlite microstructure and with the microscopic constitutive models for each of the components. Finally, the results were compared with the corresponding experimental results on both the macroscopic response and the microscopic deformation state to ascertain the validity of the numerical modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical investigation of the stress field of particulate reinforced polymeric composites subjected to tension

The aim of the present study is the detailed numerical investigation of the stress/strain distribution in polymeric matrix composites reinforced with spherical inclusions, using the finite element method (FEM). Perfect adhesion between the matrix and the inclusions was assumed and from the computed stress/strain profiles of the system, debonding initiation and propagation can easily be predicted. Analytical models available in the literature may predict the stress/strain distribution within the inclusion and along the matrix/inclusion interface, while the FEM may yield results for the whole composite, including within the inclusions. Three typical volume fractions of the composite were examined and the results were justified by the analytical predictions of other researchers. The numerical results show that the matrix starts to debond from the inclusions at angular distance forty‐five degrees and as the applied load increases the debonding zone gradually extends. Copyright © 2005 John Wiley & Sons, Ltd.     

Three‐dimensional meshfree‐enriched finite element formulation for micromechanical hyperelastic modeling of particulate rubber composites

A three‐dimensional microstructure‐based finite element framework is presented for modeling the mechanical response of rubber composites in the microscopic level. This framework introduces a novel finite element formulation, the meshfree‐enriched FEM, to overcome the volumetric locking and pressure oscillation problems that normally arise in the numerical simulation of rubber composites using conventional displacement‐based FEM. The three‐dimensional meshfree‐enriched FEM is composed of five‐noded tetrahedral elements with a volume‐weighted smoothing of deformation gradient between neighboring elements. The L₂‐orthogonality property of the smoothing operator enables the employed Hu–Washizu–de Veubeke functional to be degenerated to an assumed strain method, which leads to a displacement‐based formulation that is easily incorporated with the periodic boundary conditions imposed on the unit cell. Two numerical examples are analyzed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Weibull应力方法预测低合金钢的韧脆转化曲线

采用三参数的Weibull分布描述断裂韧度的统计规律。结合ASTM E1921-05标准,详细讨论了标准断裂试样韧脆转化曲线的建立过程;为了将标准断裂试样的测试结果用于低约束断裂试样,采用两参数的Weibull分布描述裂纹尖端局部区域的应力状态与失效概率之间的关系,并用Weibull应力将各种不同约束水平的裂纹尖端应力场联系起来,得到了预测低约束断裂试样韧脆转化曲线的公式。然后对两种A533B钢三点弯曲断裂试样进行了实例计算,进一步分析了Weibull应力的有限元计算结果,根据这些结果预测的韧脆转化曲线与试验数据相比非常吻合,证明了该文提出的方法是有效的。     

TATB填充高聚物复合材料有效热导率数值模拟

在细观层次上将1,3,5-三氨基-2,4,6-三硝基苯（TATB）/高聚物（TATB/PBX）视为由TATB颗粒、高聚物及微孔隙组成的三相复合材料。采用蒙特卡罗方法,建立了能够反映PBX细观结构的代表体积单元（RVE）模型,该模型可以生成高聚物颗粒和微孔隙随机分布、填充物体积分数和孔隙率任意调整的有限元计算（FEM）模型。研究了TATB填充体积分数、孔隙率和分布对TATB/PBX有效热导率的影响。结果表明：TATB/PBX有效热导率随着TATB体积分数的增加而增大;在相同的TATB填充体积分数下,随着孔隙率的增大,TATB/PBX的有效热导率呈指数减小,但孔隙的空间分布对有效热导率影响不大。模拟值与实验结果具有较好的一致性,证明所建二维RVE三相有限元模型可以用来预测TATB/PBX的有效热导率。     

层状复合材料磁电效应的数值分析

压电与压磁(或磁致伸缩)层合板具有大的乘积效应磁电效应。本文采用有限元分析方法对压电/压磁层合板的磁电转换进行了计算,结果表明:外磁场方向对磁电转换效应有很大的影响,在层合板上下两面增加约束可以大大提高层合板的磁电转化效应;感生电压值随压磁/压电板厚比的增加而增加,而整个层合板的电场强度值在板厚比为1时达到最大。     

Parallel implementation of implicit finite element model with cohesive zones and collision response using CUDA

The aim of this work is to efficiently implement the Park‐Paulino‐Roesler cohesive zone model with the objective of creating realistic high‐resolution simulations of material deformation, fracture, and postfracture behavior. Intrinsically, unstructured meshes can create more realistic fracture patterns in bulk material than structured meshes. Implicit methods, stable for much larger time steps, have greater potential to model both fracture and postfracture behavior without sacrificing speed of execution. Several technical contributions are presented, including (i) GPU‐accelerated implementation of the Park‐Paulino‐Roesler cohesive zone model, (ii) efficient creation of sparse matrix structure, and (iii) comparison of different unloading/reloading relations when using an implicit scheme. A potential‐based collision response scheme was implemented that allows one to model the interaction of fragmented material. Several test simulations are carried out to demonstrate the flexibility of the model and its ability to reproduce different materials under various loading conditions. Benchmarking results show that most of the computational time is spent by the third‐party solver library, meaning that other operations do not require optimization. The library is made available as open source.     

Numerical modeling of impact on wood-based sandwich structures

Abstract

The impact behavior of innovative wood based sandwich structures with plywood core and skins made either of aluminum or of fiber reinforced polymer (carbon, glass, or flax composite skins) was investigated numerically. The wood based sandwich structures were subjected to low-velocity/low-energy impacts. An explicit nonlinear numerical model based on volume elements with a cohesive layer was developed. A plastic wood law already implemented in LS-DYNA was used in association with composite type damage criteria. Comparisons with experiments in terms of layer deformations and overall contact laws during impact showed satisfactory results.     

Effect of thermomechanical treatment of 0.45 wt.% C steel in the superplastic mode on plastic zone parameters after impact fracture in the ductile-brittle transition temperature range

Transmission electron microscopy was used to study the structure of plastic zones (PZ) resulting from crack propagation during impact bending tests of a steel containing 0.45 wt.% C at +20, −40, −110 °C in the as-received state (d_g ≈ 45 μm) and after super-plastic thermomechanical treatment at intercritical temperatures (d_g ≈ 2–5 μm). Scanning electron microscopy was used to study the sample fracture surfaces. Superplastic deformation of steel was found to be responsible for the 2–6-fold increase in dislocation density in PZ induced by low-temperature plastic deformation and also the crack branching and secondary cracking as compared with the as-received state. The cold formability of the steel subjected to superplastic thermomechanical treatment can be expected to improve.     

High-Throughput Micromechanical Testing Enabled by Optimized Direct Laser Writing

Direct laser writing by two-photon lithography enables the manufacturing of tailored 3D objects, commonly referred to as 3D-printing, with submicrometer precision. Thereby, new approaches are enabled for miniaturized optical and mechanical devices, where basic material properties act as design guideline and initial input for finite element simulation-driven device design. These mechanical properties are accessible through micromechanical testing and suitably adapted miniaturized specimens. With direct laser writing, a micromechanical specimen geometry can be readily manufactured without additional postprocessing, enabling the possibility of repetitive sample production and further high-throughput testing. Widely overhanging features, as in common bending beam or tension specimens, easily cause floating layers as writing artifacts and thereby undefined geometries. Within this work, an approach to overcome this issue is presented. By introducing a slight taper within the geometry at initially printed layers, a reliable sample geometry is achievable without changing the overall mechanical behavior. As showcase geometries, miniaturized notched cantilever and advanced push-to-pull devices incorporating a notched tension specimen are detailed. Mechanical testing is conducted in situ and ex situ, and the mechanical influence from introducing a taper to a straight geometry is assessed via a finite element modeling. Thereby, a comprehensive approach for high-throughput micromechanical testing is established.     

Cohesive zone representation and junction partitioning for crystal plasticity analyses

A novel scheme is presented for incorporating finite thickness cohesive interfaces in virtual grain structures for crystal plasticity finite element (CPFE) analyses of intergranular crack initiation and propagation. A Voronoi tessellation model is used to define the virtual grain structure, with automatically generated nonzero thickness cohesive zones (CZs) representing the grain boundaries and multiple junctions. An efficient grain boundary offsetting algorithm is presented, and issues related to automatically partitioning multiple junctions are discussed. Two feasible junction partitioning schemes are presented, the second of which has the advantage of partitioning junctions using uniform quadrilateral elements and naturally defining their normal and tangential directions. For the second scheme, a rule‐based method is presented that carries out the preliminary meshing of CZ junctions, including data representation, edge event processing, and cut and trim operations. A virtual grain structure modelling system, VGRAIN, is introduced to implement the proposed CZ junction partitioning method and directly generate meshed virtual grain structures with CZ grain boundaries for CPFE studies. To demonstrate the proposed junction partitioning and CZ representation schemes, two finite strain CPFE simulations are presented for plane strain uniaxial tension and three‐point bending, demonstrating large‐scale crack initiation and propagation under shear and opening modes. Copyright © 2012 John Wiley & Sons, Ltd.     

基于有限元和神经网络的杂交建模

针对复杂非线性结构动力学系统提出了一种基于有限元与神经网络相结合的杂交建模方法。依据该方法,首先将系统中的线性结构部分采用有限元建模,非线性或难以机理建模的结构部件采用神经网络描述。其次,再通过力和位移边界联接条件将有限元模型部分和神经网络模型部分结合从而得到整个系统的杂交模型,且杂交模型的物理结构明确,精度较高,网络规模较小。在一非线性隔振系统的杂交建模算例仿真中,用所建杂交模型对正弦及宽带随机激励进行了预测检验分析,结果良好,该杂交建模方法为主体结构为线弹性结构而又包含有强非线性器件的非线性动力学系统提供了一种有效的建模途径。     

Optimizing the design of particulate composites for maximum fracture resistance through modeling

The failure modes of particulate reinforced metallic alloys are reviewed with special emphasis on in situ intermetallic particle reinforced niobium alloys, but information derived from ceramic reinforced aluminum alloys is also included. Constraint of plastic deformation by particles is emphasized as one of two very important factors in controlling fracture behavior. The other factor is particle fracture toughness. Models are proposed for describing the fracture toughness, from which several methods of enhancing toughness are envisioned. This modeling of fracture toughness is intended to help optimize the design and processing of these materials for enhanced fracture resistance. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of boron oxide on the cubic-to-monoclinic phase transition in yttria-stabilized zirconia

Specimens of yttria fully stabilized zirconia with different amounts of boron oxide have been studied by X-ray diffraction at room temperature and at higher temperatures up to 1250 °C. A boron oxide-assisted cubic-to-monoclinic phase transformation was determined in the temperature range 800-1250 °C. In situ high temperature X-ray diffraction experiments gave evidences of the dependence of the phase transformation on the heating rate. The possibility of tuning the cubic-monoclinic phase ratio by suitable addition of boron oxide before pressing and sintering is proposed.     

Mixed-Mode Delamination – Experimental and Numerical Studies

Abstract: A fracture energy approach for modelling mixed-mode delamination of composite materials and other bonded structures is introduced. The model is incorporated within an explicit finite element (FE) code and ties layered shell elements together via a stiffness condition, a failure criterion and post-failure damage law. The procedure for predictive modelling of delamination using the approach is described and the set of required input parameters is presented. A benchmark test comparing experimental results for a continuous filament random E-glass/polyester composite and explicit FE simulations for standard fracture toughness tests for a range of mode mixities is included.