Mixed-mode fracture load prediction in lead-free solder joints

Double cantilever beam (DCB) fracture specimens were made by joining copper bars with both continuous and discrete SAC305 solder layers of different lengths under standard surface mount (SMT) processing conditions. The specimens were then fractured under mode-I and various mixed-mode loading conditions. The loads corresponding to crack initiation in the continuous joints were used to calculate the critical strain energy release rate, J_ci, at the various mode ratios using elastic–plastic finite element analysis (FEA). It was found that the J_ci from the continuous joint DCBs provided a lower bound strength prediction for discrete 2 mm and 5 mm long joints at the various mode ratios. Additionally, these J_ci values calculated from FEA using the measured fracture loads agreed reasonably with J_ci estimated from measured crack opening displacements at crack initiation in both the continuous and discrete joints. Therefore, the critical strain energy release rate as a function of the mode ratio of loading is a promising fracture criterion that can be used to predict the strength of solder joints of arbitrary geometry subject to combined tensile and shear loads.     

Mixed-mode cohesive fracture of adhesive joints: Experimental and numerical studies

A broad experimental and analytical effort using fracture mechanics as the prime tool was conducted to investigate and improve the understanding of the mixed-mode cohesive fracture behavior of bonded joints. As a part of experimental efforts, mixed-mode fracture tests were performed using modified Arcan specimens consisting of several combinations of adhesive, composite and metallic adherends with a special loading fixture, in which by varying the loading angle, from 0° to 90°, mode-I, mixed-mode and mode-II fracture data were obtained. Finite element analyses were also carried out on specimens with different adherends. The main objective of this study was to determine the fracture toughness K_IC and K_IIC for a range of substrates under mixed-mode loading conditions. Another goal was to study the relationship between the stress intensity factors and the fracture toughness. Based on those analyses, mixed mode fracture criterion for the adhesively bonded systems under consideration determined. Fracture surfaces obtained at different mixed-mode loading conditions for various adherends were finally discussed.     

纤维增强复合材料层合板缺口尺寸及形状效应数值模拟

通过考虑基体裂纹、纤维断裂、层内劈裂和层间脱层等破坏形式,建立三维有限元模型研究含中心圆孔和中心裂缝的准各向同性复合材料层合板([45/0/-45/90]_(2S))在拉伸载荷下的缺口尺寸效应及缺口形状效应。模拟结果显示:随着缺口尺寸的增大,层合板的破坏强度逐渐降低,然而,在本文研究范围内含中心裂缝的层合板破坏强度始终高于对应的含中心圆孔的层合板破坏强度。进一步分析有限元模拟结果表明,含中心裂缝的层合板亚临界损伤发生得更早,并且亚临界损伤范围更大,亚临界损伤会大大缓解缺口尖端的应力集中,从而使含中心裂缝层合板表现出更高的破坏强度。     

Experimental and numerical analysis of aluminum-aluminum bolted joints subject to an indentation process

The increasing interest of the industry (especially automotive, aviation and marine) in the fastener joints (riveted, bolted, etc.) between metallic materials, has re-opened the study on the possibility to improve the performance of the drilled structure using plastic deformation processes.Indentation process, performed before the drilling operation, creates circumferential compression stresses around the hole which increase significantly the mechanical performance of the drilled structures.In this paper, static and the fatigue performances of aluminum–aluminum (AW 6082-T6) single-lap bolted joints are studied. In particular, the study compares the mechanical strength of only drilled single-lap bolted joints (OD specimens) and single-lap bolted joints subject to an indentation process (IP specimens). In order to determine the cycles to failure and the corresponding Wöhler diagram, several fatigue tests are performed. The analyses allow to determine the mechanical performance and the failure mode of the analyzed joints.Several numerical analysis, conducted in ANSYS environment on three-dimensional models of the single-lap joint, are focused on the evaluation of the residual stress on the indented plate and, in particular, to compare the stress distribution on both type of analyzed joints.     

Experimental and numerical investigations on fatigue behavior of aluminum alloy 7050-T7451 single lap four-bolted joints

The fatigue behavior of aluminum alloy 7050-T7451 single lap four-bolted joints was studied by high-frequency fatigue test and finite element (FE) methods. The fatigue test results showed that a better enhancement of fatigue life was achieved for the joints with high-locked bolts by employing the combinations of cold expansion, interference fit, and clamping force. The fractography revealed that fatigue cracks propagated tortuously; more fatigue micro-cliffs, tearing ridges, lamellar structure were observed, and fatigue striation spacing was simultaneously reduced. The evaluation of residual stress conducted by FE methods confirmed the experimental results and locations of fatigue crack initiation. The extension of fatigue lives can be attributed to the evolution of fatigue damage and effect of beneficial compressive residual stresses around the hole, resulting in the delay of crack initiation, crack deflection, and plasticity-induced crack closure.     

多钉连接钉载分配特性研究方法

利用金属-复合材料层合板紧固件多钉连接件开展拉伸载荷下钉载分配特性的试验和有限元分析研究。试验件为一列三钉单搭接和双搭接连接件。通过应变电测技术获得连接件典型截面应变分布, 再间接估算钉载分配比例。建立了试验件二维、三维有限元模型, 并计算获得应变和钉载分配结果。对比发现, 应变的计算值与实测值吻合, 但钉载分配的计算结果与实测结果存在较大偏差。分析表明: 基于表面应变测量估计钉载分配的方法不能反映连接件的附加弯矩对多钉钉载分配比例的影响; 采用经过应变测量结果验证的有限元模型, 通过数值计算确定钉载分配是一种可行的技术途径; 而应用简化的板-梁二维有限元模型计算钉载分配可以满足工程精度要求。     

Finite-element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

An elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.     

复合材料π接头拉伸力学性能的试验和计算研究

采用试验和数值模拟的方法对整体化复合材料π接头在拉伸载荷作用下的力学特性进行研究。在Instron 8803电液伺服材料试验机上进行了π接头试验件的拉伸试验,记录试验过程中损伤产生及破坏过程,记录初始失效载荷和最终失效载荷。试验结果表明,填料是π接头破坏的关键部位,需要进行深入研究。提出了复合材料π接头力学性能数值模拟的基本假设和方法,基于通用有限元商用软件,建立π接头三维力学分析模型,获得π接头各部位应力分布情况;基于基本假设,对最大应力失效准则进行修正,并给出π接头各部位损伤载荷的预测值。计算预测π接头的初始损伤部位与试验吻合,初始失效载荷计算值与5个试件试验数据均值相比误差为0.53%,表明了数值分析方法的可行性。     

大尺寸KDP晶体生长开裂的尺度效应分析

在人工生长大尺寸KDP(磷酸二氢钾,KH2PO4)晶体过程中晶体会发生开裂现象,尤其是晶体生长到400mm左右时晶帽下端容易出现裂纹.为了研究KDP晶体的生长过程中的开裂机制,采用有限元方法模拟该晶体的生长过程,重点分析了晶体在不同生长尺寸的应力场分布规律,结果表明生长过程中晶体内部应力分布存在明显的尺度效应.当KDP晶体生长达到400mm时,晶帽下部受力逐渐由受压状态转变为受拉状态,根据KDP晶体材料抗拉不抗压的性质,此时开裂的机率增大.这一发现为下一步深入研究晶体生长开裂的损伤力学机制和寻找KDP晶体生长中的防裂措施奠定了基础.     

运用应变梯度塑性理论模拟颗粒增强铝合金强度及延伸率的尺寸效应

运用基于细观机制的应变梯度塑性理论模拟了不同晶粒尺度、不同第二相颗粒直径及体积分数的铝合金应力应变曲线.结果表明,在相同条件下,随着第二相颗粒直径的减小,或随着第二相体积分数的增加,合金的强度明显增强.相反,随着第二相颗粒体积分数的增加,或随着第二相颗粒直径的减小,合金的均匀延伸率均有所下低.同时对不同晶粒尺寸的铝合金应力应变相应的分析表明,第二相颗粒分布的不均匀性对其力学性能也有一定的影响.     

微细铣削加工过程中微毛刺形成机理的模拟与实验分析

研究了采用硬质合金微铣刀铣削加工硬铝合金微槽结构时微毛刺的形成机理．建立了三维微细铣削加工硬铝合金A12024-T6的有限元模型,利用该模型动态模拟微毛刺的形成过程．分析了不同进给量与切削刃钝圆半径比值下微毛刺的形成机理,动态模拟了微槽加工过程中切削参数及切削刃钝圆半径变化对微毛刺影响的变化规律．仿真结果表明,随着每齿进给量、背吃刀量及切削刃钝圆半径的增加,微毛刺的尺寸随之增大;切削刃钝圆半径与最大有效应力是影响微毛刺尺寸的主要因素．微细铣削加工过程中,毛刺顶端所受最大有效应变明显比常规铣削加工过程中的最大有效应变高,呈现出显著的尺寸效应．通过微细铣削加工微槽实验,获得了切削参数及切削刃钝圆半径变化对微毛刺形成的影响变化规律,验证了相应有限元模型的正确性．通过数值模拟与实验方法获得了切削刃钝圆半径与毛刺尺寸（毛刺高度和毛刺厚度）的关系曲线,实验与仿真结果最大误差不超过9．8％．进一步验证了所建立的三维有限元模型适于研究并预测毛刺形成机理及毛刺尺寸的变化规律．     

Experimental and numerical characterization of low cycle fatigue and creep fatigue behaviour of P92 steel welded joint

Low cycle fatigue (LCF) and creep fatigue interaction (CFI) behaviour of P92 steel welded joint were investigated experimentally and numerically. Strain‐controlled LCF tests at different strain amplitudes and CFI tests at different peak strain holding time were conducted. Evolutions of cyclic stress response, mean stress, and creep strain during cycling were described, in which the influence of strain amplitude and holding time were investigated. A specific heat treatment process was proposed to get the homogenous simulated material of fine grain region and coarse grain region in the heat affected zone. Material parameters of parent material, fine grain heat affected zone, coarse grain heat affected zone, and weld metal in the unified viscoplasticity model were then determined and validated. To predict the LCF and CFI behaviour of welded joint, 3‐dimensional unified viscoplasticity model with a modified isotropic variable was compiled into ABAQUS UMAT. The comparison between the predicted and experimental result under LCF and CFI loadings showed that the simulation results were reasonable and agreed with the experimental data well.     

Effect of strain gradients on the size effect of concrete in uniaxial tension

A series of uniaxial tension experiments has been conducted to investigate the size effect on strength and fracture energy of quasi brittle materials like concrete and sandstone. This paper focuses on the results of the concrete tests, and specifically deals with the variation of the nominal strength for specimens of six different sizes in a scale range of 1:32. It was found that under given experimental conditions, the nominal strength strongly depended on the specimen size. More important however, is the fact that most of this size effect could be attributed to strain gradients which were present in the cross section of the specimens. These strain gradients were caused by the specimen shape, load eccentricity and material inhomogeneity. Through a combination of experimental data and a simple linear elastic analysis, the importance of strain gradients with respect to the ultimate load level could be visualized. This leads to the conclusion that studying a material size effect is not possible without taking into account structural stress/strain gradients. This revised version was published online in July 2006 with corrections to the Cover Date.     

AISI D2钢力学性能尺寸效应实验研究

为研究AISI D2钢力学性能尺寸效应现象,在常温下采用电子万能试验机和分离式霍普金森压杆(SHPB)实验装置对3种不同剪切带宽度(分别为800,400,50μm)的帽形试样进行了准静态和动态加载实验.实验结果表明,流动应力和失效应变随着剪切带宽度的减小而增大,但产生流动应力和失效应变尺寸效应现象的剪切带宽度不同.基于应变率强化项修正的Johnson-Cook本构模型,通过实验数据拟合得到材料的本构关系.研究表明,修正的Johnson-Cook本构模型与实验结果吻合较好.     

方钢管焊接空心球节点的弹性有限元分析及试验

通过有限元系统分析方钢管焊接空心球节点在轴力作用下的受力性能。建立采用实体单元的有限元模型,对轴力作用下的方钢管焊接空心球节点进行弹性有限元分析,给出轴力作用下方钢管焊接空心球节点的应力和变位分布规律,并对它的力学性能进行分析。将弹性有限元结果与试验结果进行比较,两者符合很好,验证了有限元分析的正确性。     

Lateral and vertical size effects on nanoindented microstructures

In this paper we study numerically the size effect of different constitutive relationships based on bulk silicon subjected to nanoindentation. The constitutive relationships of multilinear kinematic hardening rules are considered in order to capture elastic-perfectly plastic to strain-hardening characteristics. The size effect is estimated from the hardness of the varied contact depths normalized by that of the standard size sample that has been previously validated. Both lateral and vertical sample size effects of the microstructure are evaluated by varying respective size with an identical indentation depth. The contact depths equaling to 1/10th of the sample thickness bring around ±10% of the vertical size effect, while those equaling to one quarter lead to approximately ±20%. A softer material with an elastic-perfectly plastic characteristic generates a smaller vertical size effect because of the continuum mechanism occurs only at the near field. Narrowing down the lateral width, leads to lower loads due to no lateral boundary could conduct. Hard samples are less affected by the lateral size effect than soft ones.     

Numerical modelling and experimental investigation on welding residual stresses in large‐scale tubular K‐joints

This paper is devoted to the experimental and numerical assessment of residual stresses created by welding in the region surrounding the weld toe of tubular K‐shaped joints (i.e. region most sensitive to fatigue cracking). Neutron‐diffraction measurements were carried out on K‐joints cut from large‐scale truss beams previously subjected to high cycle fatigue. Tri‐axial residual stresses in the transverse, longitudinal and radial direction were obtained from the weld toe as a function of the depth in the thickness of the tube wall. In addition, thermomechanical analyses were performed in three‐dimensional using ABAQUS and MORFEO finite element codes. Experimental and numerical results show that, at and near the weld‐toe surface, the highest residual stresses are critically oriented perpendicularly to the weld direction, and combined with the highest externally applied stresses. Based on a systematic study on geometric parameters, analytical residual stress distribution equations with depth are proposed.     

Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts

In this article, the Coefficient of Restitution (COR) and Energy Loss Percentage (ELP) of one-dimensional impacts are determined experimentally for different ball sizes using a drop test apparatus. Ball diameters range from 6 to 12 mm, made of steel and aluminum dropped on steel and aluminum sheets.     

Analysis of fatigue crack behaviour based on dynamic response simulations and experiments for tensile-shear spot-welded joints

Fatigue crack initiation and propagation behaviours were studied based on the dynamic response simulation by the three‐dimensional finite‐element analysis (FEA) and dynamic response experiments for tensile‐shear spot‐welded joints. The entire fatigue propagation behaviour from the surface elliptical cracks at the initiation stage to the through thickness cracks at the final stage was taken into consideration during the three‐dimensional FEA dynamic response simulations. The results of the simulations and experiments found that the fatigue cracks of spot‐welded joint from initial detectable crack sizes to crack propagation behaviour could be described by three stages. Approximately one‐half of the total fatigue life was taken in stage I, which includes micro‐crack nucleation and the small crack growth process; 20% of the total fatigue life in stage II, in which the existing surface crack propagates through the thickness of sheet and 30% of the total fatigue life in stage III, during which the through thickness crack propagates along the direction of plate width to the final failure. According to the relationship between the crack length and depth and the dynamic response frequency during the simulated fatigue damage process, the definition of fatigue crack initiation and propagation stages was proposed. The analysis will provide some information for the fatigue life prediction of the spot‐welded structures.     

Experimental and numerical studies on buckling of laminated composite skew plates with circular holes under uniaxial compression

This article deals with experimental and finite element studies on the buckling of isotropic and laminated composite skew plates with circular holes subjected to uniaxial compression. The influence of skew angle, fiber orientation angle, laminate stacking sequence, and aspect ratio on critical buckling load are evaluated using the experimental method (using Methods I through V) and finite element method using MSC/NASTRAN. Method I yields the highest experimental value and Method IV the lowest experimental value for critical buckling load in the case of isotropic skew plates with circular holes. For all laminate stacking sequences considered, Method V yields the highest experimental value for critical buckling load for skew angle = 0° and Method IV yields the highest experimental value for critical buckling load for skew angles = 15° and 30°. For all laminate stacking sequences and skew angles considered, Method II yields the lowest experimental value for critical buckling load. The maximum discrepancy between the experimental values given by Method IV and the finite element solution is about 10% in the case of isotropic skew plates. The maximum discrepancy between the experimental values given by Method II and the finite element solution is about 21% in the case of laminated composite skew plates considered. The percentage of discrepancy between the numerical or finite element solution and experimental value increases as the skew angle increases. The critical buckling load decreases as the aspect ratio increases.