Multi-step 3-D finite element modeling of subsurface damage in machining particulate reinforced metal matrix composites

A multi-step 3-D finite element model using the commercial finite element packages Third Wave Systems AdvantEdge^© and ABAQUS/Explicit^© is developed for predicting the sub-surface damage after machining of particle reinforced metal matrix composites. The composite material considered for this study is an A359 aluminum matrix composite reinforced with 20 vol% fraction silicon carbide particles (A359/SiC/20p). The effect of machining conditions on the measured cutting force and damage is modeled by means of a multi-step fully-coupled thermo-mechanical model. Material properties are defined by applying the Equivalent Homogenous Material (EHM) model for the machining simulation while the damage prediction is attained by applying the resulting stress and temperature distribution to a multi-phase sub-model. In the multi-phase approach the particles and matrix are modeled as continuum elements with isotropic properties separated by a layer of cohesive zone elements representing the interfacial layer to simulate the extent of particle–matrix debonding and subsequent sub-surface damage. A random particle dispersion algorithm is applied for the random distribution of the particles in the composite. Experimental measurements of the cutting forces and the sub-surface damage are compared with simulation results, showing promising results.     

准脆性材料裂纹桥联筋的应力与变形

基于钢筋混凝土的破坏分析，结合混凝土类准脆性材料的断裂特性，本文提出了强化筋桥联基体裂纹力学分析模型，在该虚拟裂纹端部存在粘聚力分布，而强化筋在桥联裂纹处具有与基体脱离的部分段。由变形体的叠加原理和协调性条件，通过断裂力学的应力函数分析方法，推导出了在远场载荷作用下,离裂纹端部较远处桥联筋的轴向受力和变形，与脱粘筋长度之间的函数关系。文中分别就基体和强化筋材料为完全弹性，裂纹端部存在粘聚力，和强化筋为弹塑性材料等不同情况时，对裂纹和强化筋的变形和受力进行了算例分析和讨论。     

Evaluation of the interfacial strength of carbon-fiber-reinforced temperature-resistant polymer composites by the micro-droplet test

This paper presents an evaluation method for the fiber/matrix interfacial strength. The interfacial strength is determined by comparing experimental data with numerical simulations. The micro-droplet test is conducted, and the fiber axial stress at the point of interface debonding is obtained. A numerical simulation is performed with ABAQUS using an axisymmetric finite-element model. In the numerical simulation, an accurate value of the thermal residual stress based on the thermo-viscoelasticity and the damage to the resin around the blade-contacting point is considered to simulate the experimental phenomena ideally. In the thermal residual stress analysis, the actual thermal residual stress is calculated by considering the relaxation modulus and the time–temperature superposition principle for the resin. Damage initiation criteria for both dilatational and shear cases, based on continuum damage mechanics, are considered for the resin. Interfacial debonding is simulated using a cohesive zone model, and the interfacial strength is taken as the strength of the cohesive zone element at the simulated fiber maximum stress corresponding to the experimental value.     

基于微观结构的高强铝合金应力集中系数研究

为了更好地理解铝合金材料的微观力学性能,基于MATLAB编写了Voronoi算法的微观结构模拟程序,并将程序导入ABAQUS有限元软件建立铝合金晶粒模型.推导出六结点内聚线单元模型的界面单元刚度矩阵,利用内聚力模型的内聚力-位移关系描述铝合金晶粒界面间的粘着力(法向力)和摩擦力(切向力),建立了微观晶粒结构的有限元模型.研究结果表明:单个夹杂粒子随着弹性模量的增加应力集中系数先减小再增加;相对于单个夹杂粒子,两个夹杂粒子的应力集中会增加,当d/r接近2时应力集中系数明显增加,当d/r值处在6左右时应力集中系数基本恢复到单夹杂粒子时的大小.夹杂粒子的形状、数量及分布状态对结构微观应力集中均有影响.     

A new nonlocal cohesive stress law and its applicable range

In this paper, we attempt to provide a new analytical method to determine the cohesive law in the framework of nonlocal continuum mechanics. Firstly, the equivalence between the cohesive stress and the surface-induced traction (nonlocal surface residual) is established on the basis of the nonlocal stress boundary condition. Then a new cohesive stress law is derived logically from the perspective of rational mechanics, which characterizes the dependence of the cohesive stress on the crack opening displacement (COD) within the cohesive zone. Finally, we apply this new cohesive crack model to two fracture examples with different cohesive zone sizes, and investigate the stress field ahead of the crack tip in detail. The results show that the stress singularity at the crack tip is removed, and the maximum stress occurs within the cohesive zone away from the crack tip. Moreover, the stress in the large-scale cohesive zone drops rapidly to a constant approaching zero, exhibiting a stronger softening behavior.     

The effects of inter-surface cohesive tractions on linear and penny-shaped cracks

A mesoscopic fracture model of equilibrium slit cracks in brittle solids, including inter-surface cohesive tractions acting near the crack tip, is analyzed and the effects of the cohesive tractions on the in-plane stress fields, crack-opening displacement profiles, and crack driving forces examined quantitatively for linear and penny-shaped cracks. The (numerical) analysis method is described in detail, along with results for four different cohesive forces. The assumed distribution of cohesive tractions were found to suppress the in-plane stress field adjacent to cracks in a homogeneous, isotropic medium when uniformly loaded in mode-I, and the suppression was a function of crack length. The crack-opening displacement profile was also perturbed and a new regime identified between the near-field Barenblatt zone and the far-field continuum zone. The extent of this `cohesive zone' was quantified by use of an interpolating function fit to the calculated profiles and found to be independent of crack size for a given cohesive tractions distribution. Furthermore, the crack-opening displacement at the edge of the cohesive zone was found to be independent of crack size, implying that despite significant perturbations to the stress field, the crack driving force at unstable equilibrium remains unchanged with crack size.     

混凝土裂缝端部粘聚力的计算

混凝土裂缝端部断裂过程区的粘聚力分布是导致混凝土断裂呈现非线性特性的重要原因。基于混凝土的断裂特性和虚拟裂缝端部存在粘聚力的分析模型，并通过分布函数的特性分析，提出了粘聚力分布函数的两种简化表达式：一为单参数待定式，另一为双参数待定式。由变形体叠加原理，推导出计算单参数待定函数公式和计算双参数待定函数代数方程组。进而通过裂缝张开位移实测数据即可求得粘聚力分布，并且给出了适当的算例分析和讨论。     

Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression

The mechanical behavior of unidirectional fiber-reinforced polymer composites subjected to tension and compression perpendicular to the fibers is studied using computational micromechanics. The representative volume element of the composite microstructure with random fiber distribution is generated, and the two dominant damage mechanisms experimentally observed – matrix plastic deformation and interfacial debonding – are included in the simulation by the extended Drucker–Prager model and cohesive zone model respectively. Progressive failure procedure for both the matrix and interface is incorporated in the simulation, and ductile criterion is used to predict the damage initiation of the matrix taking into account its sensitivity to triaxial stress state. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the tension fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation, while the compression failure is dominated by matrix plastic damage. And then the effects of interfacial properties on the damage behavior of the composites are assessed. It is found that the interfacial stiffness and fracture energy have relatively smaller influence on the mechanical behavior of composites, while the influence of interfacial strength is significant.     

A modified cohesive zone model for a high‐speed expanding crack

The present work studies a self‐similar high‐speed expanding crack of mode‐I in a ductile material with a modified cohesive zone model. Compared with existing Dugdale models for moving crack, the new features of the present model are that the normal stress parallel to crack faces is included in the yielding condition in the cohesive zone and traction force in the cohesive zone can be non‐uniform. For a ductile material defined by von Mises criterion without hardening, the present model confirms that the normal stress parallel to crack face increases with increasing crack speed and can be even larger than the normal traction in the cohesive zone, which justifies the necessity of including the normal stress parallel to the crack faces in the yielding condition at high crack speed. In addition, strain hardening effect is examined based on a non‐uniform traction distribution in the cohesive zone.     

FINITE ELEMENT SIMULATION OF METAL CUTTING CONSIDERING CHIP BEHAVIOR AND TEMPERATURE DISTRIBUTION

The finite element method was used for simulating orthogonal metal cutting of low-carbon steel. The model predicts chip geometry, behavior of the metal under machining, cutting force values, stress distribution, and temperature distribution along the workpiece and the chip. Separation and the friction action between the chip and tool were simulated using a friction slideline capability. The same technique was applied to the undeformed chip-workpiece interaction zone to simulate the separation between the chip and the workpiece. The model considered the thermal effect and the friction along the tool rake face. Force values predicted from this model were compared with some experimental work for the same material at the same range of cutting speed and show good correlation.     

基于粘聚区模型的含填充区复合材料接头失效数值模拟

建立了Ⅰ型与Ⅱ型失效模式耦合的粘聚单元本构模型, 并通过模拟双悬臂梁实验进行了验证。将粘聚单元插入填充区任何2 个实体单元之间, 预测填充区的随机裂纹, 模拟了接头在拉伸载荷下的失效。计算了复合材料基体、界面胶膜、填充物3 者不同强度、填充区半径、填充物刚度等多种情况下接头的拉伸失效。计算结果表明: 复合材料基体、界面胶膜、填充物3 者的强度显著影响接头的承载能力与失效模式; 随着填充区半径增大, 结构承载能力也随之提高。试验结果验证了模拟结果。      

A Cohesive Zone Approach for Fatigue-Driven Delamination Analysis in Composite Materials

A new model for prediction of fatigue-driven delamination in laminated composites is proposed using cohesive interface elements. The presented model provides a link between cohesive elements damage evolution rate and crack growth rate of Paris law. This is beneficial since no additional material parameters are required and the well-known Paris law constants are used. The link between the cohesive zone method and fracture mechanics is achieved without use of effective length which has led to more accurate results. The problem of unknown failure path in calculation of the energy release rate is solved by imposing a condition on the damage model which leads to completely vertical failure path. A global measure of energy release rate is used for the whole cohesive zone which is computationally more efficient compared to previous similar models. The performance of the proposed model is investigated by simulation of well-known delamination tests and comparison against experimental data of the literature.     

On the Cohesive Zone Model for a Finite Crack

The paper concentrates on the development of the crack tip model with the cohesive zone in an infinite plate with a finite crack of mode I. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration according to Westergaard's theory with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. The calculation results of the crack tip opening displacement are compared with the Dugdale solution for the plane stress. This revised version was published online in July 2006 with corrections to the Cover Date.     

Interface fracture in adhesively bonded shell structures

Two methods for the prediction of crack propagation through the interface of adhesively bonded shells are discussed. One is based on a fracture mechanics approach; the other is based on a cohesive zone approach. Attention is focussed on predicting the shape of the crack front and the critical stress required to propagate the crack under quasi-static conditions. The fracture mechanical model is theoretically sound and it is accurate and numerically stable. The cohesive zone model has some advantages over the fracture mechanics based model. It is easier to generalise the cohesive zone model to take into account effects such as plastic deformation in the adhering shells, and to take into account effects of large local curvatures of the interface crack front. The comparison shows a convergence of the results based on the cohesive zone model towards the results based on a fracture mechanics approach in the limit where the size of the cohesive zone becomes smaller than other relevant geometrical lengths for the problem. However, convergence issues and numerical stability must be addressed.     

基于弹-塑-断裂理论的镐型截齿截割机理研究与实验验证

为研究镐型截齿在截割煤岩过程中的截割机理,建立镐型截齿外轮廓的数学模型,基于弹性力学、塑性力学和断裂力学等理论,提出了煤岩截齿截割力作用下发生弹-塑-断裂失稳理论模型,以此来描述截齿截割煤岩机理,并依据理论模型分别推导出煤岩在弹性变形、塑性变形和断裂失稳状态下截齿截割力以及煤岩应力表达式。最后采用自主搭建实验设备进行不同截割倾角的镐型截齿截割煤岩实验,实验结果表明:煤岩在截齿截割力作用过程中,随着截齿截割深度的增加,截齿与煤岩的接触面积逐步增大,煤岩存在弹性变形阶段、塑性变形阶段以及断裂失稳阶段并与理论模型相符;截割倾角为90°、75°、60°时,截齿截割阻力理论值与实验值的均方根误差分别为0.082 kN、0.199 kN、0.204 kN,理论值与实验值相差较小,验证理论模型的正确性。     

A nonlocal cohesive zone model for finite thickness interfaces – Part I: Mathematical formulation and validation with molecular dynamics

A nonlocal cohesive zone model is derived taking into account the properties of finite thickness interfaces. The functional expression of the stress–separation relationship, which bridges the gap between continuum damage mechanics and nonlinear fracture mechanics, depends on the complex failure phenomena affecting the material microstructure of the interface region. More specifically, the shape of the nonlocal cohesive zone model is found to be dependent on the damage evolution. On the other hand, damage is in its turn a function of dissipative mechanisms occurring at lower length scales, such as dislocation motion, breaking of interatomic bonds, formation of free surfaces and microvoids, that are usually analyzed according to molecular dynamics. Hence, the relationship intercurring between the parameters of the damage law and the outcome of molecular dynamics simulations available in the literature is also established. Therefore, the proposed nonlocal cohesive zone model provides also the proper mathematical framework for interpreting molecular dynamics-based stress–separation relationships that are typically nonlocal, since they always refer to a finite number of atom layers.     

基于界面断裂的粘聚区长度计算方法研究

基于各向异性双材料界面断裂力学理论,再根据D-B模型假设的有限裂纹尖端奇异性将消失,推导出复合材料分层裂纹尖端粘聚区长度的计算模型。结果显示复合材料分层裂纹尖端粘聚区具有振荡性(当振荡因子0时),并且粘聚区长度与裂纹长度、应力值及振荡因子有关。将新模型应用于界面单元法中,模拟了双悬臂梁(DCB)和混合型弯曲梁(MBB)分层扩展过程中的载荷-位移关系,并比较了不同的粘聚区长度对收敛性和计算精度的影响,结果表明该模型可较精确地计算复合材料的粘聚区长度,以此为基础划分网格能同时保证收敛性和计算精度要求,并可有效地节省运算时间。     

Experimental Investigation on Rotary Ultrasonic Face Grinding of SiCp/Al Composites

SiCp/Al composites have been widely used in many fields such as aerospace, automobile, advanced weapon system, etc. But this kind of material, especially with high volume fraction, is difficult to machine due to the reinforced particles existing in matrix, which has limited its further application. Rotary ultrasonic machining (RUM) has many excellent features and it has never been used to machine SiCp/Al composites. In order to improve the machinability and application of SiCp/Al composites, the rotary ultrasonic face grinding experiments of SiCp/Al composites reinforced with 45% volume SiC particles were carried out to investigate cutting force, surface quality, tool wear, and abrasive chip shapes. The experimental results indicate that ultrasonic vibration could reduce cutting force, surface roughness, surface defects, and increase plastic removal ratio. The cutting force could be lowered by an average of 13.86% and the surface roughness could be lowered by an average of 11.53%. The examined results of tool wear patterns suggest that tool wear is mainly caused by grain breakage and grain fall-off. Grinding wheel blockage and grinding burn were not observed in machining process.     

短纤维复合材料宏微观内聚力模型参数测量的实验与数值混合法

提出了一种改进的实验与数值混合法。该方法采用随机短纤维增强复合材料的紧凑拉伸实验,首先得到材料的宏观内聚力模型,进而确定该材料纤维基体界面微观内聚力模型参数。通过有限元法和基于场投影的反解法得到了宏观内聚力模型结果,对比分析这两个方法的结果,得出该反解法对误差的容忍度较低。随后采用改进的反解法,用数字图像相关法(DIC)直接获取宏观内聚力模型分离量,减少了该反解法未知数的数量,提高了容错率。再将DIC和改进的反解法结合,对该材料裂纹尖端宏观内聚力区的牵引力进行了反解。采用双线性内聚力模型,根据Mori-Tanaka方法,将求得的宏观内聚力定律与纤维基体界面微观内聚力定律关联起来,从而求得了纤维基体界面微观内聚力模型参数。该方法和结果可为短纤维增强复合材料纤维基体界面的微观力学分析提供实验基础。     

Cohesive Fracture Model Based on Necking

A linear hardening model together with a linear elastic background material is first used to discuss some aspects of the mathematical and physical limitations and constraints on cohesive laws. Using an integral equation approach together with the cohesive crack assumption, it is found that in order to remove the stress singularity at the tip of the cohesive zone, the cohesive law must have a nonzero traction at the initial zero opening displacement. A cohesive zone model for ductile metals is then derived based on necking in thin cracked sheets. With this model, the cohesive behavior including peak cohesive traction, cohesive energy density and shape of the cohesive traction–separation curve is discussed. The peak cohesive traction is found to vary from 1.15 times the yield stress for perfectly plastic materials to about 2.5 times the yield stress for modest hardening materials (power hardening exponent of 0.2). The cohesive energy density depends on the critical relative plate thickness reduction at the root of the neck at crack initiation, which needs to be determined by experiments. Finally, an elastic background medium with a center crack is employed to re-examine the shape effect of cohesive traction–separation curve, and the relation between the linear elastic fracture mechanics (LEFM) and cohesive zone models by considering the cohesive zone development and crack growth in the infinite elastic medium. It is shown that the shape of the cohesive curve does affect the cohesive zone size and the apparent energy release rate of LEFM for the crack growth in the elastic background material. The apparent energy release rate of LEFM approaches the cohesive energy density when the crack extends significantly longer than the characteristic length of the cohesive zone.