Total Equivalent Strain Research Articles

Equivalent stress and total strain range predictions for multiaxial states of stress and strain

The paper describes a procedure for modifying finite element predictions of equivalent stress and equivalent total strain in order to obtain equivalent stress and equivalent total strain ranges for lowcycle fatigue life estimates.

Evaluation of Phase Growth Process in Sn/Pb Eutectic Solder under Thermal Cyclic Loading.

Thermal fatigue damage of solder joint is considered to be closely related to microstructural coarsening. In the present study, phase growth model is devised in order to express the microstructural evolution of Sn/Pb eutectic sobder. The model is based on results of systematic microstructural abservation using lap joint type shear specimen proposed by the authors. And the model is also derived from the vacancy diffusion theory in phase boundary. The phase growth is characterized by parameter S which is defined as average phase size to the 4 th power d4 and increases approximately proportional to time and total equivalent creep strain. Furthermore, the model is applied to evaluation of phase growth process in the solder joint of the specimen under thermal cyclic loading which realizes approximately thermal deformation state of printed circuit board (PCB). Consequently, it is clarified that phase growth proceeds at any temperature to which PCB is subjected and is mainly induced by strain rather than thermal equilibrium. And parameter S increases corresponding to total equivalent creep strain. This suggests that S would be evaluation parameter for thermal fatigue damage of actual solder joint.

Analytical and Experimental Hybrid Study on Thermal Fatigue Strength of Electronic Solder Joints. 1st Report. Rationalization of Accelerated Thermal Cyclic Test and Evaluation of Thermal Fatigue.

Stress-strain analyses for Sn-Pb cutectic solder joints in a thin single outline package (STOP), a ball grid array (BGA) assembly, and a leadless ceramic chip carrier (LCCC) were carried out for investigation of plastic-creep behavior, and of stress relaxation behavior due to accelerated thermal cycling tests or the operating conditions. the temperature dependence of plastic behavior (yield stress) and creep behavior (creep properties) were taken into account in all numerical analyses. The results of finite element analysis (FEA) show that in an accelerated terperature cycling test, long high-temperature and low-temperature dweel times do not contribute to an increase in the cyclic inelastic equivalent strain range in solder joints, although the creep behavior occurring during the dwell times under operating conditions is very important in estimation of the fatigue life of solder joints. Based upon the results of the strain analyses, an efficient temperature cycling test process for microelectronic solder joints was proposed, and cycling tests were carried out. The experimental results show that the thermal fatigue life of microelectronic Sn-Pb eutectic solder joints can be predicted by an associated fracture parameter of total equivalent inelastic strain range, and the fatigue life of solder joints follows Coffin-Manson's law.

Microstructure and texture evolution of Al during hot and cold rolling

The evolution of microstructure and texture of commercial purity Al during hot and cold rolling has been studied. The results show that the dynamic restoration mechanism for Al rolled to a total equivalent strain of 2.66 at a mean equivalent strain rate of 14.4 s-1 at 510 °C is essentially dynamic recrystallization (DRX), whereas for those materials deformed to lower strains at lower strain rates at this temperature, the restoration mechanism is mainly dynamic recovery (DRV). This is confirmed by examining the microstructures, textures, and substructures of the material developed during hot rolling as well as by comparing the results with those developed during cold rolling and annealing. The texture analysis using orientation distribution functions (ODFs) indicates that the dynamically recrystallized material has a random orientation distribution, whereas dynamically recovered materials have a developed deformation texture with a predominantD component and a Cu component. The substructure observation by transmission electron microscopy (TEM) indicates that the subgrains in the dynamically recrystallized material are completely dynamically recovered, which is very similar to those subgrains in cold-rolled material. However, the annealed material shows a completely different substructure. By studying all of these structural features, which are closely associated with the dynamic restoration mechanism, it is confirmed that Al undergoes DRX in the present work, which is different from either DRV or static recrystallization (SRX).

Finite Element Modeling of Orthogonal Metal Cutting

The finite element method was used to model chip formation in orthogonal metal cutting. Emphasis was given on analyzing the effect of important factors, such as plastic flow of the workpiece material, friction at the tool-workpiece interface, and wear of the tool, on the cutting process. To simulate separation of the chip from the workpiece, superposition of two nodes at each nodal location of a parting line of the initial mesh was imposed. According to the developed algorithm, the superimposed nodes were constrained to assume identical displacements, until approaching to a specified small distance from the tool tip. At that juncture, the displacement constraint was removed and separation of the nodes was allowed. Under the usual plane strain assumption, quasi-static finite element simulations of orthogonal metal cutting were performed for interfacial friction coefficients equal to zero, 0.15, and 0.5 and unworn or worn (cratered) tools having a strongly adherent built-up edge. To investigate the significance of the deformation of the workpiece material on the cutting process, elastic-perfectly plastic and elastic-plastic with isotropic strain hardening and strain rate sensitivity constitutive laws were used in the analysis. For simplicity, the tool material and the built-up edge were modeled as perfectly rigid. In all cases analyzed, the cutting speed and depth of cut were set equal to 183 m/min and 1.27 mm, respectively. Experiments confirmed that cutting of AISI 4340 steel with ceramic-coated tools under similar conditions led to the development of a built-up edge and the formation of continuous chips. The dimensions of the crater, assumed in the finite element simulations involving a cratered tool, were also determined from the same cutting experiments. Spatial distributions of the equivalent total plastic strain and the von Mises equivalent stress corresponding to steady-state cutting conditions and the normal and shear stresses at the rake face are contrasted and interpreted qualitatively in terms of critical parameters. The influence of interfacial friction, metal flow characteristics, and wear at the rake face of the tool on the steady-state magnitudes of the cutting forces, shear plane angle, chip thickness, and chip-tool contact length are also elucidated. Several aspects of the metal cutting process predicted by the finite element model agreed well with experimental results and phenomenological observations.

Tribological transitions phenomena of ceramic materials : Woydt, M., Klaffke, O., Habig, K.-H. and Czichos, H.Wear Mar. 1990 136, (2), 373–380

A set of strain-controlled biaxial proportional and non-proportional tests were conducted on solid and tubular specimens of 30CrNiMo8HH steel. The effect of the phase angle on fatigue life was studied. This effect becomes noticeable when applying a 90° out-of-phase loading, reducing the fatigue life by a factor up to 5. It has been shown that the material has no additional hardening due to out-of-phase loading. To account for this severe path dependency, a material dependent non-proportionality modification factor is proposed. This path dependent sensitivity factor is applied to six different fatigue parameters including maximum equivalent total strain, maximum equivalent stress, Smith–Watson–Topper, Fatemi–Socie, plastic strain energy density and total strain energy density to correlate the fatigue results. The predicted fatigue lives are compared with the experiments. The cyclic plasticity models of Mroz and Chaboche were successfully employed to model the cyclic behavior of 30CrNiMo8HH steel. It has been shown that estimations based on the proposed non-proportionality modification factor agree well with the experimental results.

Discussion des critères macroscopiques de rupture recherche d’un critère macroscopique d’amorçage

The criteria for ductile fracture proposed by Latham and Cockroft and by Oyane are applied to the following deformation paths: simple shear then uniaxial tension (C + T), or the opposite (T + C). The results of both criteria are very similar, the path C + T giving a smaller total equivalent strain. The shapes of the critical curves for decohesion obtained from a microscopic model suggest the formulation of a macroscopic criterion for the initiation of damage similar to the macroscopic criteria for fracture.

A Study on Metallic Creep-Fatigue Interaction at Elevated Temperatures : Especially, Based on Strain History

In order to investigate the difference between the hold-time effect in push-pull low-cycle fatigue and that in torsional one, both types of strain controlled fatigue tests of SUS 316 stainless steel were performed at 600°C with or without hold-time. Significant difference between the push-pull and torsional fatigue test data on the basis of equivalent total strain range of Mises' type was not observed in terms of number of cycles to failure, number of cycles to crack initiation and crack propagation rate. More precisely speaking, however, the push-pull test had a larger hold-time effect on the failure life and on the crack behaviors than the torsional test in lower strain range. That is, slower crack propagation rate was observed in the push-pull test without hold-time than in torsional one, but crack propagation was observed in the push-pull test with hold-time. This crack behavior was discussed from the influence of stress triaxiality near the crack tip on the crack propagation rate and also from the effect of hydrostatic stress.

A Study on Thermal Fatigue of Circular Disk : in connection with the strength of Gas Turbine Disk

The analytical and experimental results of thermal fatigue of a circular disk of structural carbon steel are presented. The periphery of the disk is cycled between two programmed temperature levels, while a water cooled sink at the inner radius is kept at lower temperature level. (1) Unsteady elasto-plastic thermal stress and the strain in the disk specimen calculated from the measurement of radial temperature distribution on the disk are in good agreement with the experimental results, in both the measurement of the diametral displacement and the X-ray residual stress measurement. (2) Number of cycles to initiation of thermal crack in the disk is predicted from the uniaxial thermal fatigue test data on the common basis of the equivalent total strain range of Mises' criterion. The propagation rate of thermal crack is also predicted on the basis of product of the rate (dl/dN) with the number of cycles N at a prescribed crack length l.

Thermal Fatigue under Multiaxial Thermal Stresses

Experimental investigation on multiaxial thermal fatigue was performed by using solid spherical and cylindrical specimens of low carbon steel. The specimens were subjected to cyclic multiaxial thermal stresses introduced by repeated heating and cooling processes. The uniaxial thermal cycling tests and mechanical strain cycling tests at elevated temperature were also conducted on the same material, and the relationship between the strength of material under three types of cycling were studied.The thermal strain range containing plastic strain of multiaxial thermal fatigue has been analyzed by means of successive approximation. Taking account of the fact that the cracks nucleate and propagate on the surface of the specimen, Mises' equivalent total strain on the surface is considered to be the strain range that determines the lifetime of the material subjected to the multiaxial thermal stress cyclings. For the purpose of elucidating the relationship between these three types of strength, the basis for the criterion of lifetime in terms of the number of cycles to crack initiation, constraint of thermal strain and equivalent steady temperature has been established as variables. The comparison between the three types of test results are made by using these common bases.From the fact that the results of multiaxial thermal fatigue tests by the use of both solid spherical and cylindrical specimens are in good correlation with the uniaxial thermal and mechanical fatigue test results, the following conclusion has been made. The strength of the material subjected to multiaxial thermal stress cycling can be predicted from the information of conventional tests, namely, the uniaxial thermal fatigue test under the same constraint of thermal strain as that of the multiaxial thermal cycling, or the uniaxial mechanical fatigue test at equivalent steady temperature.

鋼塊の加熱過程における熱応力について

During the heating process thermal stress arises in the steel ingot because of two main causes; i. e. the temperature difference within the ingot and the volume change caused by the transformation.In this report author tried to relate theoretically the method of calculating the thermal stress under high temperature. As the deformation under high temperature is accompanied by not only elastic strain but plastic strain also, it is very difficult to determine the thermal stress. Here the author denotes the deformation in elastic-plastic range by a nonlinear integral equations and by introducing the conception of equivalent total strain he calculates the stress and the plastic strain through a comparatively easy successive integration.For the calculation of the stress during transformation range the author regards the curve of the expansion values as three straight lines and these three lines denote the three stages of transformation i. e. the pre-, mid- and post-transformation stage and so he makes calculation according to these three stages. And he calculates the stress and plastic strain which occur when the transformation progresses from the surface to the core.Two calculated examples are shown of high-carbon-chromium steel circular ingots at two stages; one is where the ingot is undergoing the transformation and the other is where the ingot has no relation with transformation.The following facts have been discovered by this theoretical calculation;(1) As for the stress distribution there is compression stress (σr=0, σt=σz) in the outer part of the ingot and tension stress (σz≅2σr=2σt) near its core and the stress is greatest at the core in the heating process, because of high surface temperature.(2) During the transformation the tension stress which has been greatest at the core decreases in accordance with the progress of transformation for the time, but from the beginning of transformation of the core till its completion there occurs a violent increase of the stress and plastic strain and the elastic stress becomes the greatest of all the stages.So if some crackings take place in this case, it can be inferred that discus-form crackings will occur normal to the axis near the core when the core completes the transformation.