Maximum Equivalent Plastic Strain Research Articles

Enhancing the Reliability of Wafer Level Packaging by Using Solder Joints Layout Design

During the design and manufacturing processes of electronic packaging, solder joints are fabricated using a variety of methods to provide both mechanical and electrical connections for different applications. They include flip chip, wafer level chip scale packaging (WLCSP), fine pitch ball grid array (BGA), and chip scale packaging (CSP). The solder joint shape prediction methods have been incorporated as a design tool to enhance the reliability of the WLCSP. However, the reliability of solder joints for a large chip size such as 10mmtimes10mm without underfill remains questionable. In this research, a hybrid method combining an analytical algorithm with the energy-based approach is applied to predict standoff heights and geometry profiles of the solder joints. In addition, a hybrid-pad-shape system is proposed to design the solder ball layout, and to enhance the reliability of the solder joints. Next, a nonlinear and parametric finite element analysis is conducted to investigate the reliability issues that result from several design parameters. In addition, an experimental validation is completed to verify the correctness and feasibility of the solder joint shape prediction methods and finite element analysis procedures. The design parameters considered in this study include solder joint layout, solder volume, pad diameter, as well as the ratio and orientation of the elliptical pad. With regards to solder joint layout design, the solder joints located in the corner areas can be considered as structural dummy balls with no electrical signals passing through them. The results reveal that when the WLCSP has large round pads, or properly oriented elliptical solder joint pads at the corner areas underneath the chip, then the maximum equivalent plastic strain of the solder joints will be effectively reduced. As a result, the solder joint fatigue life under thermal loading will be greatly enhanced. Furthermore, the findings of this research can be used as a design guideline for electronic packaging with area array interconnections such as CSP, flip chip packaging, Super CSP, and fine pitch BGA

The simulation of deformation distribution during ECAP using 3D finite element method

In this paper, a 3D finite element model is used to analyse the deformation heterogeneity during a single pass of equal channel angular pressing (ECAP). The equivalent plastic strains in three perpendicular planes of the billet are predicted and the influence of the friction between billet and channel on the equivalent plastic strain is determined. The results show that the equivalent plastic strains are not uniform in three directions. The deformation inhomogeneity indexes and the location of maximum equivalent plastic strain are varied with the increasing friction coefficient. The numerical predictions have a good agreement with theoretical and experimental results. This indicates that the proposed 3D finite element model can perfectly simulate the deformation distribution during ECAP process.

Modeling of failure near spot welds in lap-shear specimens based on a plane stress rigid inclusion analysis

In this paper, the failure mechanism of resistance spot welds in dual-phase steel lap-shear specimens is investigated based on experimental observations, two-dimensional elasticity theories and two-dimensional finite element analyses. Optical micrographs of the cross sections of spot welds in lap-shear specimens of a dual-phase steel before and after failure are first examined to understand the failure mechanism. The experimental results suggest that under lap-shear loading conditions, a necking failure is initiated near the middle of the nugget circumference in the base metal and then the failure propagates along the nugget circumference in the sheet to final fracture. Based on the stress function approach of the elasticity theory, an analytic solution for an infinite plate containing a rigid inclusion subjected to a resultant shear force is developed and used to investigate the stress and strain distributions near the nugget in lap-shear specimens. The results of the elastic analytic solution and those of a two-dimensional elastic finite element analysis indicate that the initial yielding starts on the two side edges of the inclusion in the sheet. However, the results of a two-dimensional elastic–plastic finite element analysis indicate that as the applied displacement increases, the maximum equivalent plastic strain shifts from the two side edges of the inclusion to the middle of the inclusion along the inclusion circumference in the sheet. The computational results suggest that the location of the initial necking failure should occur near the middle of the nugget circumference in the sheet as observed in experiments based on the forming limit diagram (FLD) for ductile sheet metals.

Constant and Variable Amplitude Cyclic Plasticity in 316L Stainless Steel

In this paper, cyclic plastic behavior of 316L stainless steel has been investigated through uniaxial experiments. An elasto-plastic material model is proposed that builds on a Chaboche based model that is readily available in commercial FE-software. The model has been calibrated for 316L through cyclic symmetric strain experiments for a strain range up to 4%. Experiments show that strain loading history and strain range have a significant impact on the behavior of the material. The plasticity model available in FE-codes only depends on the maximum equivalent plastic strain though. More complex material models require a significant number of parameters to be calibrated and require extensive experiments to provide the required calibration data. For most applications this calibration effort is too extensive. To include both phenomena of strain history and strain range dependency, at least in a basic manner, a user subroutine was created that aids the material model in describing these dependencies.

117 半導体微細はんだ接合部の疲労き裂発生と進展寿命評価(疲労)

The fatigue crack growth life and the crack path of micro fillet-shaped solder joints were evaluated by using functions of the fatigue J-integral ΔJ_f and the creep J- integral ΔJ_c , and by applying the criterion Δσ_<θ, max> on ΔJ_I and ΔJ_II. A new auto-mesh generator, which attaches the fine mesh around a crack tip to the original mesh without a crack, was developed for effectively preparing a new mesh pattern of an extended crack. There were much difference in the predicted crack path by criteria of a strain energy density, maximum tangential stress range and equivalent plastic strain range. However the crack path could be successfully predicted by Δσ_<θ, max>. The calculated crack extension life of the solder joints showed considerable difference, because of the comparable effects in the cyclic and time dependency of crack growth.

Transferability of critical condition for ductile cracking in bent small scale specimen to evaluation of critical internal pressure for ductile cracking in axially notched linepipe

For two types of API 5L X65 linepipes, the critical conditions for ductile cracking of the linepipe steel and their applicability to the evaluation of the ductile cracking of an axially notched linepipe were investigated. Static three point bending tests and finite element (FE) analyses for a Charpy V notch specimen were conducted to evaluate the critical conditions for ductile cracking from the notch tip. At the position of ductile cracking for the Charpy specimen, the calculated stress triaxiality was almost constant for both linepipe steels; however, the equivalent plastic strain for each linepipe steel was different. Hydrostatic burst tests were then conducted for internally patched linepipes with an axial through wall notch. The results of FE analyses for the hydrostatic burst tests indicated that the maximum equivalent plastic strain value within the wall thickness was almost the same as that obtained from the three point bending test in the Charpy V notch specimen. It was therefore ascertained that the critical conditions for ductile cracking of linepipes with an actual notch can be predicted from the results of a small scale test and FE analysis, which are used to evaluate the relationship between the stress triaxiality and the equivalent plastic strain.

Contact Fatigue Analysis of an Elastic-Plastic Layered Medium With a Surface Crack in Sliding Contact With a Fractal Surface

Contact fatigue of a layered medium consisting of an elastic surface layer and three elastic-plastic underlying layers in sliding contact with a rigid and rough surface was analyzed with the finite element method. To include multiscale roughness effects and self-affine surface features, the topography of the rough surface was characterized by scale-invariant fractal geometry. A contact algorithm was used to identify the critical segment of the rough surface to be used in the contact fatigue simulations. The tensile and shear stress intensity factors and the direction and dominant mode of crack growth were determined from the crack-tip stresses. The effect of surface cracking on the evolution of plasticity in the second layer and the significance of topography (fractal) parameters on crack growth are interpreted in terms of the contact pressure, stress intensity factors, and maximum equivalent plastic strain. It is shown that a transition from tensile to shear dominant mode of fatigue crack growth occurs as the crack tip approaches the interface, resulting in further crack growth almost parallel to the layer interface. The obtained results illustrate the important role of surface roughness in contact fatigue of layered media.

Effects of solder joint structure and shape on thermal reliability of plastic ball grid array package

Among the PBGA (plastic ball grid array) packages, a 72-I/O OMPAC (overmolded effect array carrier) package is studied during thermal cycling. The ANSYS software is applied to analyze the effects of some factors on the solder joint for the fatigue life due to elastoplastic deformation of the electronic package; those factors are solder structure, shape, and pitch. The result shows that the maximum equivalent plastic strain range occurs at two interfaces, one is between the solder joint and the substrate, another one is between the solder joint and the printed circuit board. Moreover, the solder shape is determined by the solder height and the pad diameter under a fixed value of solder volume. It is found that the convex-shaped solder with larger height and smaller pitch has smaller maximum equivalent plastic strain range, which leads to the longer fatigue life. In addition, there are two kinds of solder structure: pure solder joint and copper core solder joint. In the copper core solder joint, the eutectic part becomes so small that a larger strain is induced. Therefore, the pure solder joint has smaller maximum equivalent plastic strain range and longer fatigue life than the copper core solder joint.

Analysis of the spherical indentation cycle for elastic–perfectly plastic solids

A finite element analysis of frictionless indentation of an elastic–plastic half-space by a rigid sphere is presented and the deformation behavior during loading and unloading is examined in terms of the interference and elastic–plastic material properties. The analysis yields dimensionless constitutive relationships for the normal load, contact area, and mean contact pressure during loading for a wide range of material properties and interference ranging from the inception of yielding to the initiation of fully plastic deformation. The boundaries between elastic, elastic–plastic, and fully plastic deformation regimes are determined in terms of the interference, mean contact pressure, and reduced elastic modulus-to-yield strength ratio. Relationships for the hardness and associated interference versus elastic–plastic material properties and truncated contact radius are introduced, and the shape of the plastic zone and maximum equivalent plastic strain are interpreted in light of finite element results. The unloading response is examined to evaluate the validity of basic assumptions in traditional indentation approaches used to measure the hardness and reduced elastic modulus of materials. It is shown that knowledge of the deformation behavior under both loading and unloading conditions is essential for accurate determination of the true hardness and reduced elastic modulus. An iterative approach for determining the reduced elastic modulus, yield strength, and hardness from indentation experiments and finite element solutions is proposed as an alternative to the traditional method.

Prediction of static fracture strength of laser-welded lap joints by numerical analysis

The purpose of this study is to investigate whether experimental results of static fracture strength of lap joint made by laser welding can be predicted by numerical analysis or not. First, numerical analytical method was devised for estimating the experimental result of the relationship between load and displacement of shear test. Next, experimental result of static fracture strength was predicted by using the concept of critical equivalent plastic strain, that the lap joint is fractured when maximum equivalent plastic strain reaches a critical value. The static fracture strength of lap joint was predicted by the concept of critical plastic strain when fracture occurs in the base metal. However, when lap joint was broken by shear fracture in the joint part, shear strength of lap joint could not be predicted by the concept. The shear strength of lap joint could be predicted from the shear strength of weld metal.

A study of post-form static and fatigue properties of superplastic 7475-SPF and 5083-SPF aluminium alloys

The intention of this work was to derive conditions for superplastic forming of aircraft skin components to eliminate or minimise the deleterious effects of cavitation, so to meet design criteria, and thus to qualify superplastic forming as a forming technique for the manufacture of aircraft structural components. Two aluminium alloys were chosen for investigation, 7475-SPF (Formall 700) and 5083-SPF (Formall 545), supplied by Alusuisse Swiss Aluminium, in sheets of 1.6 and 2 mm thickness, respectively. These were chosen as representative of a high strength precipitation hardening alloy liable to cavitation and a solid solution alloy chosen for formability. A press was built permitting manual control of temperature, forming pressure and back-pressure. To assist selection of the forming conditions for the chosen component, the frictional behaviour of the two target alloys was measured and the forming process was simulated by the finite element method (FEM) using the implicit version of the ABAQUS™ [ABAQUS, Hibbitt, Karlsson and Sorenson Inc., RI, USA] FE package. Post-form properties of the superplastically formed component—thickness distribution, cavitation, static strength and fatigue strength—were studied to qualify the component for use in aircraft structures. It was shown that a maximum of 46% reduction in thickness occurred in the trial component. Cavitation was suppressed by using a back-pressure of 2 MPa, approximately 10 times the forming pressure. This compares with flow stresses of 3 and 5 MPa for 7475-SPF and 5083-SPF, respectively, under such conditions. Because the maximum equivalent plastic strain was limited to approximately to 0.8, relatively few cavities (1–2 vol.%) were formed. These reduced the tensile strength by only about 5%, but the effect on ductility was substantially greater, about 20%. Annealing after forming had limited effect on the post-forming properties of the alloys because it caused only some of the small cavities to sinter. However, in the T6 condition, the fatigue strength of 7475-SPF alloy formed under a back-pressure of 2 MPa was retained.

Cavity mediated strain localization and overall ductility in eutectic tin-lead alloy

A combined experimental and numerical study is undertaken to examine the effects of pre-machined holes on strain localization and overall ductility in eutectic tin-lead alloy. Thin-sheet specimens with equal-sized holes aligned in the tensile loading direction are used. The tensile tests were performed at room temperature with a nominal strain rate of 0.001 s−1. The specimen, containing one hole, showed a significant reduction in ductility compared to the control (no-hole) specimen. With an increasing number of holes, however, the overall strain-to-failure increases and fracture tend to follow shear bands generated locally from the hole edges. Finite element analyses, taking into account the viscoplastic response, were carried out to provide a mechanistic rationale to corroborate the experimental findings. The dispersion of plastic deformation and the effect of hole interaction are both found to contribute to the observed behavior. The local maximum equivalent plastic strain decreases with increasing number of holes, resulting in more delayed fracture. Plastic deformation becomes more intense inside the shear band when the holes are spaced more closely, which explains the increasing propensity of fracture along the shear bands in specimens containing more pre-machined holes.

数値解析によるレーザ重ね継手の静的強度予測

The purpose of this study is to investigate whether experimental results of static fracture strength of lap joint made by laser welding can be predicted by numerical analysis or not. First, numerical analytical method was devised for estimating the experimental result of the relationship between load and displacement of shear test. Next, experimental result of static fracture strength was predicted by using the concept of critical equivalent plastic strain, that the lap joint is fractured when maximum equivalent plastic strain reaches a critical value. The static fracture strength of lap joint was predicted by the concept of critical plastic strain when fracture occurs in the base metal. However, when lap joint was broken by shear fracture in the joint part, shear strength of lap joint could not be predicted by the concept. The shear strength of lap joint could be predicted from the shear strength of weld metal.

The effect of constraint-induced normal stress on the failure of notched TiAl components

Titanium aluminides are candidates for replacing nickel superalloys in some aircraft engine components. In uniaxial tension tests, these materials experience plastic strains at failure that place them in-between traditional definitions for ductile and brittle materials. This study considers the appropriate continuum mechanics failure criterion for these materials under multiaxial loading conditions (based on either the maximum equivalent plastic strain or the maximum normal stress). The material tested is a Ti-47.0Al-2.0Cr-1.9Nb alloy having a predominantly lamellar γ/α 2 microstructure. Cylindrical notched tensile specimens that experience elevated normal stresses in their interiors due to circumferential constraint during plastic deformation have been investigated. Results are presented that quantify reductions in failure loads due to elevated normal stress, compared to those predicted by finite element models using a maximum equivalent plastic strain criterion. To properly interpret the experimental results, the effects of notch strengthening must be included in the model predictions. Model and experimental results suggest that this TiAl alloy has some sensitivity to normal stress and that a combined failure criterion is needed to accurately predict failure under multiaxial loading conditions. A fracture initiation and failure mechanism requiring a combination of normal stress and plastic straining is suggested that is consistent with observed features at fracture initiation sites.

Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges

This paper investigates the elastic-plastic seismic behavior of long span cable-stayed steel bridges through the plane finite-element model. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the stay cable sag effect, axial force-bending moment interaction, and large displacements. Material nonlinearity arises when the stiffening steel girder yields. The example bridge is a cable-stayed bridge with a central span length of 605 m. The seismic response analyses have been conducted from the deformed equilibrium configuration due to dead loads. Three strong earthquake records of the Great Hanshin earthquake of 1995 in Japan are used in the analysis. These earthquake records are input in the bridge longitudinal direction, vertical direction, and combined longitudinal and vertical directions. To evaluate the residual elastic-plastic seismic response, a new kind of seismic damage index called the maximum equivalent plastic strain ratio is proposed. The results show that the elastic-plastic effect tends to reduce the seismic response of long span cable-stayed steel bridges. The elastic and elastic-plastic seismic response behavior depends highly on the characteristics of input earthquake records. The earthquake record with the largest peak ground acceleration value does not necessarily induce the greatest elastic-plastic seismic damage.

Application of coupled brittle–ductile model to study correlation between Charpy energy and fracture toughness values

A coupled brittle–ductile fracture local approach model has been developed to predict either Charpy energy or fracture toughness and to investigate conditions for correlations between them. A modification to the Beremin model has been introduced to assess failure in individual elements and make it compatible with the Lemaitre model for implementation as a user subroutine for the program ABAQUS. A probabilistic based fracture criterion was introduced to monitor the damage within individual elements by either cleavage or ductile tearing. The fracture toughness and Charpy energy for a nuclear industry steel BPL A508 were determined for the transition temperature range using finite element analyses with three-dimensional solid elements for both the standard 25 mm SE(B) three-point bend specimen and the Charpy 45° V-notch specimen. Prescribed failure probabilities of 0.05, 0.5 and 0.95 were imposed as critical values to predict the scatter of fracture toughness experimental data. The evaluation of constraint, equivalent plastic strain and maximum principal stress amongst other parameters gave the basis for comparison of the response of the two geometries. Critical values of fracture stress in the modified Beremin model for cleavage fracture and of the Lemaitre damage parameter for ductile fracture were calibrated from experimental fracture toughness data. These same critical values were then used in the analysis of the Charpy specimens, including allowance for strain rate effects, and good agreement found between predicted and experimental energy absorption values. The only conditions where the maximum constraint and equivalent plastic strain in the two specimen geometries were found to match were at the temperature for 28 J energy absorption in the Charpy impact energy and that for fracture toughness, KIC, of 100 MPa-m1/2 for the BPL A508 steel. This may be an important factor in the correlation between Charpy and fracture toughness tests proposed by Wallin.

A computational study of the relations between material properties of long-rod penetrators and their ballistic performance

The paper summarizes a series of two-dimensional numerical simulations which were performed to study the effects of material properties on the terminal ballistics of long-rod penetrators. Our focus was on the properties of the rod material, unlike recent works which concentrated on a target’s properties. We varied almost all the relevant parameters within a large range of values in order to study the separate effects of each one. These parameters included: compressive and tensile strengths, elastic moduli, melting temperatures and the maximum equivalent plastic strain (failure strain) of the rod material. Most of the simulations were performed for an actual experiment with 300 mm tungsten-alloy long-rod, impacting a semi-infinite steel target. The simulations show that the mechanical and thermal softening mechanisms are the most dominant, as far as the depth of penetration is concerned. In contrast, the elastic moduli and spall strength have a negligible effect as far as penetration depth is concerned.

Analysis of Ultramicrohardness by Conical Indenter. 2nd Report. Influence of Indenter Tip Radius on Surface Deformation Characteristics.

Deformation around concavity created by indentation of a conical indenter in an ultramicrohardness tester is analyzed using FEM computer simulation. Effects of indenter tip radius on concavity shape and hardness from concavity depth both under loading and load-free conditions in soft material which has low yield stress and high work hardening rate are examined. The results obtained are as follows. (1) Concavity created by a conical indenter is sinking-in type including concavity rim. The larger tip radius and the deeper concavity depth make concavity rim more unclear. The maximum elastic recovery is at the bottom of concavity. (2) At the same depth the applied load increases linearly with tip radius. (3) An increase in tip radius makes the plastic zone broader and the maximum equivalent plastic strain at the bottom of concavity lower. The stress field around the concavity is compressive. (4) Correction of errors at the indenter tip is effective to a conical indenter with tip radius 0∼3μm.

The Impact of Interfacial Adhesion on PTH and Via Stress State

In this paper the impact of the state of barrel-laminate adhesion on the PTH and via stresses is investigated. A representative PTH and a representative blind via in a printed wiring board are used as demonstration vehicles. Transient heat conduction and nonlinear elastic-plastic-contact finite element analyses are carried out on PTHs and vias under the extreme conditions of perfect and zero barrel-laminate adhesion. In general, the maximum equivalent plastic strains in PTHs and vias with strong barrel-laminate adhesion are not large enough to fracture the plating. Fracture is possible at or near the innerplane junction when barrel-laminate adhesion is lost. The possibility of plating fracture in a blind via is strongly dependent on the tolerances in manufacturing process parameters such as drill depth and laminate thickness.

Numerical simulation of penetration of aluminum targets by spherical-nose steel rods

Numerical simulations of the penetration processes in aluminium blocks by spherical-nose steel rods were performed in this study. The specific impact configuration of this study involves 152-mm diameter 6061-T651 aluminum bars impacted by spherical-nose projectiles machined from T-200 maraging steel rods at nominal impact velocities between 300 and 1000 m/s. The transient dynamic finite element code LS-DYNA2D was used for the numerical analysis. The erosion capability in LS-DYNA2D was exercised in conjunction with the maximum equivalent plastic strain criterion to carry out failure simulations in the target. Calculated results were compared to the experimental data. Good correlation was obtained.