Inelastic Strain Range Research Articles

Thermal Fatigue Life Prediction of BGA Solder Joint Incorporating Microstructural Coarsening Effect due to Thermal Diffusion.

A creep constitutive equation incorporating the effect of microstructure coarsening was introduced into the Finite Element Method analysis using a user subroutine to predict thermal fatigue life of solder joint. Dispersed particles in the microstructure grew due to thermal diffusion with increasing fatigue cycles, which resulted in the inelastic strain range and the inelastic strain energy density range increased. This increase in the inelastic strain range reduced the fatigue life by approximately 77% compared to the case where no microstructure coarsening effect was incorporated. Thus, it is necessary to incorporate the microstructure coarsening effect in the fatigue analysis of solders. Thermal fatigue life was found to be significantly affected by the microstructure coarsening effect. Thus, it is necessary to incorporate the microstructure coarsening effect in the fatigue analysis of solders.

Characterization of plastic and creep behavior in thick aluminum wire for power modules

One of the common reliability concern on most of power modules is a failure of its bonding. Stress, strain, and displacement fields around those bonding in power modules are required for highly-reliable design based on physically/mechanically based failure model. They can be accurately obtained from CAE tools such as finite element computer codes for stress analysis with mechanical properties of materials not only in the elastic region but also in the inelastic region. In this paper, for the reliability study of an aluminum bonding wire, an experimental study was performed to acquire its plastic and creep characteristics. The temperature-dependent constitutive equations for plastic and creep behavior of an aluminum wire are presented based on the isothermal tensile test data. These constitutive equations can be used at the temperatures ranging from 20 °C to 250°C, and are useful for estimating fatigue life predictions of bonding wires, when we utilize the failure models based on the physical quantities such as the inelastic strain range, the inelastic strain energy density range, the nonlinear fracture mechanics parameter T* range and so on.

Review of Methodologies for Structural Integrity Evaluation of Power Modules

AbstractThis paper reviews the previous research on the methodologies for evaluating structural integrity of wire bonds and die-attachments in power modules. Under power module operation, these parts are subjected to repeated temperature variations which induce repeated thermal stress due to the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. Thus, thermal fatigue phenomena are critical issues for the structural integrity of power modules. In the present paper, we also deal with the evaluation methodologies for thermal fatigue in the temperatures over 200 °C, which are expected operational temperatures for wide bandgap semiconductor power modules. The failure models based on the temperature range ΔT widely used in the power electronics community are critically reviewed from a mechanical engineering viewpoint. Detailed discussion is given concerning the superiority of failure models based on the physical quantities such as the inelastic strain range Δεin, the inelastic strain energy density range ΔWin, and the nonlinear fracture mechanics parameter range ΔT* over the conventional ΔT-based failure models. It is also pointed out that the distributed state concept (DSC) approaches based on the unified constitutive modeling and the unified mechanics theory are promising for evaluating the structural integrity of power modules. Two kinds of test methods, a power cycling test (PCT) and a thermal cycling test (TCT), are discussed in the relation to evaluating the lifetimes of wire-liftoff and die attach cracking.

A modified constitutive model for tensile deformation of 9%Cr steel under prior fatigue loading

Reliable constitutive models are necessary for the precise design and manufacture of complicated components. This study is devoted to developing a modified constitutive model to capture the effects of prior fatigue loading on subsequent tensile deformation of 9%Cr steel. In the proposed model, a strain hardening rule combined with a defined fatigue damage parameter was introduced to represent prior fatigue damage. The defined fatigue damage parameter based on the inelastic strain range of each cycle is capable of describing the evolution of tensile strength, recovery of martensite laths and decline of dislocation density, regardless of the variation in fatigue loading conditions. To validate the predictive capacity of the proposed model, experimental tensile results at different strain amplitudes, lifetime fractions and hold times of prior fatigue loading were compared with the predicted results. Good agreement between experimental and predicted results indicates that the proposed model is robust in describing the tensile behaviour under prior fatigue loading. Moreover, few determined material parameters are required, which makes the proposed model convenient for practical applications.

Thermomechanical fatigue in 9-12Cr steels: Life prediction models and the effect of tensile dwell periods

This paper is concerned with the assessment of life prediction models for thermomechanical fatigue (TMF), with specific application to P91 steel. A program of TMF tests, including dwell periods, are performed to determine the role of thermomechanical loading on fatigue life. As expected, fatigue life under conventional TMF testing (no dwells) is governed by maximum applied stress and inelastic strain-range. However, with the introduction of dwell periods, at maximum tensile stress during TMF loading, in-phase loading becomes the life-limiting case. This is attributed here to increased microstructural degradation and oxidation, associated with the dwell at peak temperature. Analysis of commonly used TMF life prediction models shows that the effect of dwell periods currently cannot be predicted for in-phase loading. Thus, it is concluded that physically-motivated approaches are required to successfully predict fatigue life under more complex (service) thermomechanical loading histories.

Thermo-mechanical fatigue behavior of nickel-based 23Cr-45Ni-7W alloy for boiler pipes and tubes

This study focuses on thermo-mechanical fatigue (TMF) behaviors of nickel-based 23Cr-45Ni-7W alloy for pipes and tubes in high-efficiency power boilers. TMF tests (maximum temperature = 700 °C; minimum temperature = 100 °C) were conducted under in-phase (IP) and out-of-phase (OP) conditions. The lives under the IP condition is 0.30–0.44 times of that under the OP condition when same total strain range, Δεt, is applied. The TMF properties obtained via the tests are compared with the results of isothermal fatigue (ITF) tests conducted at 700 °C and bithermal fatigue (BTF) tests with maximum and minimum temperatures of 700 °C and 100 °C, respectively. The fracture morphology for each type of TMF, ITF, and BTF is similar under the test conditions of this study. Intergranular cracking is predominant under application of cyclic tensile creep strain during the fatigue tests, and transgranular cracking is predominant under application of cyclic compressive creep strain during the fatigue tests. The inelastic strain range–fatigue life (Δεin–Nf) relation in the TMF test and the inelastic strain range components–life (Δεij–Nij) relation determined using the strain range partitioning method show a good agreement within a factor of 1.5 scatter band. These results indicate the possibility of predicting the TMF life of the 23Cr-45Ni-7W alloy using the results of the ITF test by considering the amount and direction (tension or compression) of creep strain applied to the alloy.

GS0318 小型せん断試験片による非弾性ひずみ範囲の取得に関する研究

GS0318 小型せん断試験片による非弾性ひずみ範囲の取得に関する研究

パワーモジュールにおける信頼性評価の考え方

This paper describes the methodology for reliability evaluation of power semiconductor devices. When they are used in power systems, they are subjected to thermal cycles caused by power fluctuations. In such circumstances, power modules break down because of wire-liftoff in wire-bond and solder crack in dye-bond induced by thermal fatigue. In most papers concerning power electronics, such thermal fatigue life Nf has been related with temperature range ΔT together with the mean temperature Tm during cycling. The Nf -ΔT relation depends on the dimensions of power modules, even if they are made of the same materials. On the other hand, the Manson-Coffin rule correlating Nf with inelastic strain range Δεin or inelastic strain energy density ΔWin is independent of the dimensions of power modules. This paper presents how to obtain the Manson-Coffin rule from thermal fatigue experiments of power modules. In addition to the mechanical reliability problems described above, the present paper describes the importance of an electrical reliability problem of power devices, in which the electronic performance of semiconductor power devices is adversely affected by the action of stress.

G0300101 鉛フリーはんだラップジョイント型せん断試験片による非弾性ひずみ範囲取得方法の提案

G0300101 鉛フリーはんだラップジョイント型せん断試験片による非弾性ひずみ範囲取得方法の提案

Fatigue Life Estimation of Lead-Free Solder Joints Using Viscoplastic-Creep Separate Constitutive Model

When we estimate the fatigue life of lead-free solder joints under cyclic temperature load, we have to get equivalent inelastic strain range accurately. In this study, in order to show the example of using our previously proposed constitutive model, which can describe stress strain curves, stress strain hysteresis loops and stress relaxation curves, with these temperature dependencies and these rate dependencies, we conducted FE analysis of the chip component under thermal cycle using the constitutive model. We also conducted fatigue tests of Sn3.5Ag0.5Cu0.07Ni0.01Ge lead-free solder using micro test pieces and estimated the fatigue life.

Influence of Extremum Temperatures on TMF of a Ni-Base Superalloy

Significantly reducing the minimum temperature while maintaining maximum temperature of thermomechanical fatigue (TMF) cycles can reduce the life even when mechanical strain ranges are similar. This applies to in-phase (IP) and out-of-phase (OP) TMF cycles. This reduction in life has generally been attributed to a combination of changes in microstructure arising from aging and increases in the cyclic inelastic strain promoted by increases in the elastic modulus as the minimum cycle temperature is reduced. TMF cycles under both IP and OP conditions were conducted with maximum cycle temperatures within the 750-950C range and with minimum cycle temperatures of either 100 or 500C. A reduction in minimum temperature was observed to promote a decrease in TMF life by as much as a factor of ten for all TMF experiments. The reduction in TMF life is primarily controlled by increases in the inelastic strain range associated with increases in the elastic modulus that arise when the minimum temperature is reduced.

J0310205 高剛性ラップジョイントせん断試験によるはんだ接合部の疲労き裂発生寿命評価([J031-02]電子情報機器・半導体デバイス・電子部品の冷却技術(2),材料力学部門)

Shear fatigue tests of Sn-3.0Ag-0.5Cu solder joints were carried out by the combination of an advanced lap-joint specimen with high stiffness fixtures. This paper presents an evaluation of fatigue crack initiation lifetime of the joints under the condition of low strain rate followed by creep deformation. Consequently, an experimental relation between the inelastic strain range and the number of cycles corresponding to 20% load decrease were obtained.

Improvement of water slot design for beam blank casting mould

Two-dimensional thermo–elastic–plastic creep finite element models of two beam blank moulds with different water slot designs, the large hole mould and the small hole mould, are set up and their thermomechanical behaviour is numerically investigated by means of ABAQUS software. The temperature, distortion, stress and inelastic strain range across the hot faces as well as the fatigue life of the two moulds are discussed in detail, based on which it is shown that the distributions of temperature and distortion of the small hole mould are more uniform than those of the large hole mould, and the peak temperature of the former mould is smaller than that of the later mould. However, the fatigue life of the small hole mould is shorter than that of the large hole mould. Both moulds were put into service in an industry and it is demonstrated that the quality of the product cast by the small hole mould is better than that by the large hole mould, and the service life of the small hole mould is longer than that of the large hole mould because the service life of a mould chiefly depends on the wear of its hot face, which is much shorter than the fatigue life. An improved water slot design for the beam blank mould is then proposed and it is numerically demonstrated that this improved mould is superior to the large hole mould and the small hole mould.

The Reliability of Solder Joints in Fine Pitch 3-D Stack Package by Taguchi Method

To achieve high density and high performance, through-Silicon Vias (TSVs) have recently aroused much interest because it is a key enabling technology for three-dimensional (3-D) integrated circuit stacking and silicon interposer technology. In this study, a 3-D 1/8th symmetrical nonlinear finite element model of a stack die TSV package was developed using ANSYS finite element simulation. The model was used to optimize the package for robust design and to determine design rules to enhance 3-D stack package in view of bump reliability. An L8(2×7) Taguchi matrix was developed to investigate the effects of interposer thickness, TSV diameter, insulation (SiO2) thickness, chip thickness, substrate thickness, bump height, and bump diameter on bumps reliability. A temperature cycling test in the range of 0 °C to 100 °C was conducted by three cycles. The mechanical property of SAC leadless solder included time independent plastic and time dependent creep behaviors. The parameter of inelastic strain range of the third cycle was used to evaluate the bump life prediction. Two levels were chosen for each parameter to cover the ranges of interest. The results show that the smaller insulation (SiO2) and substrate thickness and the larger dimension for the other factors provide the best combination. These could be used as guides for further similar 3-D stack packages design.

Thermomechanical fatigue and bithermal–thermomechanical fatigue of a nickel-base single crystal superalloy

Thermomechanical fatigue (TMF) is a critical damage process incurred by turbine components. The most common methods for simulating the operating conditions of turbine components are either in-phase (IP) or out-of-phase (OP) TMF tests. However, due to the constantly changing temperature and applied load profile, it is challenging to decouple dominant damage mechanisms occurring in the material when relying solely on TMF test conditions. Further, the time to perform low(er) inelastic strain range TMF tests to failure can be cumbersome. This work proposes implementation of bithermal fatigue (BiF) tests to address these issues. Out-of-phase BiF tests are strain-controlled fatigue tests whereby a single cycle consists of an isothermal compressive half-cycle at the maximum temperature, followed by stress-free temperature change to the minimum temperature; the tensile half-cycle then occurs isothermally at the minimum temperature, followed by stress-free temperature change to the maximum temperature. Both conventional OP TMF and OP BiF tests were performed on nominally 〈001〉 oriented single crystal superalloy specimens. When plotting test results as inelastic strain range versus cycles to crack initiation, the OP BiF results exhibit a clear demarcation from the TMF data at a particular value of inelastic strain range; above which the results are primarily fatigue dominated and follow the trend of the OP TMF tests while below the results are environmentally dominated, creating a separate trend. Thermally-activated base material degradation supports the theory of damage driver segregation. A relationship is proposed relating the inelastic strain of BiF to that of TMF, for identical lives, within the environmentally dominated fatigue region. Finally, a life prediction model is proposed that includes fatigue and environmentally assisted damage mechanisms, which enables the life estimation of either test type. These relationships enable the use of BiF tests in place of, or in conjunction with, TMF tests, thereby providing insight into the dominant damage mechanisms present during testing and simplifying life prediction for more complex TMF cycles.

A Probabilistic Approach to Predict Thermal Fatigue Life for Ball Grid Array Solder Joints

Numerous studies of the reliability of solder joints have been performed. Most life prediction models are limited to a deterministic approach. However, manufacturing induces uncertainty in the geometry parameters of solder joints, and the environmental temperature varies widely due to end-user diversity, creating uncertainties in the reliability of solder joints. In this study, a methodology for accounting for variation in the lifetime prediction for lead-free solder joints of ball grid array packages (PBGA) is demonstrated. The key aspects of the solder joint parameters and the cyclic temperature range related to reliability are involved. Probabilistic solutions of the inelastic strain range and thermal fatigue life based on the Engelmaier model are developed to determine the probability of solder joint failure. The results indicate that the standard deviation increases significantly when more random variations are involved. Using the probabilistic method, the influence of each variable on the thermal fatigue life is quantified. This information can be used to optimize product design and process validation acceptance criteria. The probabilistic approach creates the opportunity to identify the root causes of failed samples from product fatigue tests and field returns. The method can be applied to better understand how variation affects parameters of interest in an electronic package design with area array interconnections.

Endurance Life and Deformation Behavior under Thermo-mechanical Fatigue of Nb-added Heat Resistant Austenitic Stainless Steel

Thermomechanical fatigue (TMF) behavior of heat resistant austenitic stainless steel was evaluated in the temperature range from 100°C to peak temperatures of 600 to 800°C; The fatigue lives under TMF conditions were plotted against the plastic strain range and the dissipated energy per cycle. In the expression of the inelastic strain range versus fatigue life, the TMF data obtained at different temperature ranges were located close to a single line with a small deviation; however, when the dissipated energy per cycle, calculated from the area of the stress-strain hysteresis loops at the half of the fatigue life, was plotted against the fatigue life, the data showed greater scattering than the TMF life against the inelastic strain range. A noticeable stress relaxation in the stress-strain hysteresis curve took place at the peak temperatures higher than 700°C, but all specimens in this study exhibited cyclic hardening behavior with TMF cycles. Recrystallization occurred during the TMF cycle concurrent with the formation of fine subgrains in the recrystallized region, which is considered to cause the cyclic hardening of the steel. (Received March 29, 2011)

A comparative study on thermomechanical and low cycle fatigue failures of a single crystal nickel-based superalloy

The cyclic deformation and lifetime behaviors of a single crystal nickel-based superalloy CMSX-4 have been investigated under out-of-phase thermomechanical fatigue (OP TMF) and isothermal low cycle fatigue (LCF) conditions. OP TMF life exhibited less than a half of LCF life although smaller inelastic strain range and lower mean stress level during OP TMF were observed compared to those during LCF. During OP TMF cycling, the maximum tensile strain at the minimum temperature was found to accelerate the surface crack initiation and propagation. Additionally, the multiple groups of parallel twin plates near crack provided a preferential path for crack propagation.

Analysis of Stress-Strain Hysteresis Loop and Prediction of Thermal Fatigue Life for Chip Size Package Solder Joints

The aim of this study is to investigate the relationship between the inelastic strain range and the thermal fatigue lives of chip size package solder joints with Sn-Pb and Sn-Ag-Cu solder balls. The inelastic strain range was examined by finite element analysis. In both solder joints, the exponential terms in the inelastic strain range term in the Coffin-Manson equation were evaluated as 1.8 - 2.3. These values are very close to the conventional one used in Sn-Pb and the Pb containing solders. The inelastic strain range is almost proportional to the temperature range in the Sn-Pb solder joint. On the contrary, the inelastic strain range is proportional to approximately the square root of the temperature range in the Sn-Ag-Cu solder joint. The deference depends on the change of the stress-strain hysteresis curve in the thermal cycle.

Damage development of Al/SiC metal matrix composite under fatigue, creep and monotonic loading conditions

A consolidation of powders using the KOBO method at elevated temperature was elaborated for production of Al/SiC metal matrix composite (MMC). The observations of the mean strain and inelastic strain range during the force controlled high cycle fatigue (HCF) tests identified the ratcheting mechanism combined with mechanism characterized by cyclic plasticity. Damage parameters were calculated on the basis of strain signal acquisition during fatigue tests. Fatigue properties, creep resistance and lifetime of Al/SiC MMC were gradually improved with the increase of the SiC particles content. The microstructural observations of the material before and after tests were also performed.