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The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The anticipated unified propagation function describes the infinitesimal crack-length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification functions with different number of fitting parameters are proposed. On one hand, the closed-form analytical solutions facilitate the universal fitting of the constants of the fatigue law over all stages of fatigue. On the other hand, the closed-form solution eases the application of the fatigue law, because the solution of nonlinear differential equation turns out to be dispensable. The main advantage of the proposed functions is the possibility of having closed-form analytical solutions for the unified crack growth law. Moreover, the mean stress dependence is the immediate consequence of the proposed law. The corresponding formulas for crack length over the number of cycles are derived.

In this paper, the method of representation of crack propagation functions through appropriate elementary functions is employed. The choice of the elementary functions is motivated by the phenomenological data and covers a broad region of possible parameters. With the introduced crack propagation functions, differential equations describing the crack propagation are solved rigorously.

The resulting closed-form solutions allow the evaluation of crack propagation histories on one hand, and the effects of stress ratio on crack propagation on the other hand. The explicit formulas for crack length over the number of cycles are derived.

In this paper, linear fracture mechanics approach is assumed.

Shortening of evaluation time for fatigue crack growth. Simplification of the computer codes due to the elimination of solution of differential equation. Standardization of experiments for crack growth.

This paper introduces the closed-form analytical expression for crack length over number of cycles. The new function that expresses the damage growth per cycle is also introduced. This function allows closed-form analytical solution for crack length. The solution expresses the number of cycles to failure as the function of the initial size of the crack and eliminates the solution of the nonlinear ordinary differential equation of the first order. The different common expressions, which account for the influence of the stress ratio, are immediately applicable.

widely‐used hypoelastic model for four well‐known objective stress rates under a four‐phase stress cycle associated with axial tension and/or torsion of thin‐walled cylindrical tubes. Here, two kinds of models based upon the Cauchy stress and the Kirchhoff stress will be treated. The reduced systems of differential equations of these rate constitutive equations are derived and studied for Jaumann, Green‐ Naghdi, logarithmic and Truesdell stress rates, separately. Analytical solutions in some cases and numerical solutions in all cases are obtained using these reduced systems. Comparisons between the residual deformations are made for different cases. It may be seen that only the logarithmic stress rate results in no residual deformation. In particular, results indicate that Green‐Naghdi rate would generate unexpected residual deformation effect that is essentially different from that resulting from Jaumann rate. On the other hand, it is realized that this study accomplishes an alternative, direct proof for the nonintegrability problem of Truesdell’s hypoelastic rate equation with classical stress rates. This problem has been first treated successfully by Simo and Pister in 1984 using Bernstein’s integrability conditions. However, such treatment needs to cope with a coupled system of nonlinear partial differential equations in Cauchy stress. Here, a different idea is used. It is noted that every integrable hypoelastic equation is just an equivalent rate form of an elastic equation and hence should produce no residual deformations under every possible stress cycle. Accordingly, a hypoelastic model with a stress rate has to be non‐integrable, whenever a stress cycle can be found under which this model generates residual deformation. According to this idea of reductio ad absurdum, a well‐designed stress cycle is introduced and the corresponding residual deformations are calculated. Unlike the treatment of Bernstein’s integrability conditions, it may be a simple and straightforward matter to calculate the final deformations for a given stress cycle. This has been done in this study for several well‐known stress rates.

The purpose of this paper is to develop an approach to optimize the cycles‐to‐failure of a peened component with respect to laser peening (LP) variables: pressure magnitude, mid‐span, and spot size when the component is subject to a variable amplitude loading.

To optimally design an LP process, an experimentally validated 3D finite element simulation of the LP process, a cycles‐to‐failure estimation capability incorporating residual stress, and a particle swarm optimization strategy were developed and employed to maximize the cycles‐to‐failure of a component of a titanium turbine disk.

The most critical finding of this research is that a minor difference in the residual stress profile can lead to a large difference in the cycles‐to‐failure. This finding implies that selecting the optimization objective to be the cycles‐to‐failure is a better option as compared to the residual stress profile.

The LP‐induced residual stresses are assumed static and do not change as number of load cycles increase.

The paper develops a framework that relates the LP variables and the cycles‐to‐failure of a peened component. A modified particle swarm optimization approach is developed to optimize the fatigue life of a turbine disk.

THE work described in this paper was undertaken to investigate the behaviour of a magnesium alloy beam clastically and plastically deformed by a uniform bending moment at room temperature. The object of the work was to obtain relations between stresses and strains in the beam, to afford a basis for design, in cases where it is required to submit magnesium alloy structures to bending stresses exceeding the elastic limit.

The purpose of this paper is to determine: how the thermal cycling aging affects the ratcheting behavior of anisotropic conductive adhesive film (ACF); how the loading conditions and loading history affect the ratcheting strain and strain rate of ACF with different thermal cycling aging histories.

The ACF of CP6920F was cured at 190°C in an electro-thermal vacuum drying apparatus for 30 s. The cured specimens were put into the thermal cycling chamber (−40-150°C) for aging to 25, 50, 100, 200 and 500 cycles. A series of uniaxial ratcheting tests of aged ACF after different thermal cycles was carried out under stress control at 80°C.

The ACF subjected to larger number of thermal aging cycles exhibits less ratcheting strain under the same loading conditions. The ACF with the same thermal cycling aging history shows more ratcheting strain and a higher ratcheting strain rate when loaded under a larger mean stress or stress amplitude or a lower loading rate. The ratcheting behavior of aged ACF is found to be more sensitive to the lower loading rate. The higher mean stress (or stress amplitude) enhances the deformation resistance and consequently restrains the ratcheting strain of subsequent cycling with a lower mean stress (or stress amplitude). The prior lower loading rate accelerates the plastic deformation more significantly than the higher one.

The influencing trends of thermal cycling aging, loading condition and loading history on ratcheting behavior of ACF are obtained, which is important for the design and safety assessment of ACF joints.

To understand the roles of service‐related parameters, such as imposed cyclic strain amplitude and cyclic strain rate, on the stress relaxation behaviour of eutectic Sn‐Ag solder joints.

Cyclic shear straining with associated stress relaxation at the shear strain extremes imposed was carried out on pre‐strained eutectic Sn‐Ag solder joints with various cyclic shear straining conditions. Results from such experiments were compared with previously reported findings from monotonic shear straining and stress relaxation tests.

At higher testing temperatures with a larger cyclic strain amplitude, stress states realized at the subsequent cycle are comparable with, or even gradually increase on, those experienced at the previous cycle, especially after few cycles. The maximum shear stress obtained at each cycle and residual stress during stress relaxation are strongly affected by cyclic strain rate. Stress relaxation during subsequent cycles of straining was found to be strongly dependent on the test temperature, and the imposed cyclic strain amplitude and cyclic strain rate.

In this paper, the experiments were carried out on eutectic Sn‐Ag solder joints with about a 100 μm joint thickness, which are, therefore, representative of those used in microelectronics. Also, there is no systematic study reporting the effects of cyclic straining conditions on the stress relaxation behaviour of eutectic Sn‐Ag solder for this joint configuration in the published literature.

WHERE service life, cither actual or simulated, has proven to be inadequate, the need for a simple conversion of fatigue cycles to service life is paramount. The task becomes exceedingly difficult in the case of service life where neither number nor magnitudes of loads can be determined. The only known quantity is that the machine or structure lasted only one‐tenth, one‐third, or not quite as long as it should.

The purpose of this paper is to compare mechanical response of polypropylene in multi‐cycle tensile tests with strain‐controlled and mixed deformation programs and to develop constitutive equations that describe quantitatively the experimental data.

Multi‐cycle tensile tests are performed on isotactic polypropylene with strain‐controlled (oscillations between fixed maximum and minimum strains) and mixed (oscillations between a fixed maximum strain and the zero minimum stress) programs. A constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and its parameters are found by fitting observations. The effect of damage accumulation of material parameters is analyzed numerically.

The model predicts accurately mechanical behavior of polypropylene in tests with numbers of cycles strongly exceeding those used to determine its parameters. In the regime of developed damage, material constants in the stress‐strain relations are independent of deformation program.

A novel constitutive model is derived in cyclic viscoelastoplasticity of semicrystalline polymers and comparison of its adjustable parameters is performed for different deformation programs.

The purpose of this paper is to investigate the behavior of compressive residual stress induced by laser peening under external loading on an age‐hardened high‐strength aluminum alloy A2024‐T3, a low‐carbon austenitic stainless steel SUS316L (Type 316L) and a nickel‐based alloy NCF600 (Alloy 600).

The surface residual stress was measured intermittently by X‐ray diffraction during cyclic uniaxial loading.

The compressive residual stress due to laser peening significantly decreased during the first few cycles at stress ratio of 0.1 with the maximum loading stress exceeding the 0.2 per cent yield stress. No remarkable decrease was observed afterward until the end of the loading cycles.

Under symmetric loading at the stress ratio of −1 to A2024‐T3, a major decrease took place in the compression side of the first loading cycle. The surface residual stresses remained in compression within all the extent of the present experiments, even if the maximum loading stress exceeded the yield stress of the materials.

The purpose of this paper is to present the durability analysis in predicting the reliability life cycle for an automobile crankshaft under random stress load using the stochastic process. Due to the limitations associated with the actual loading history obtained from the experimental analysis or due to the sensitivity of the strain gauge, the fatigue reliability life cycle assessment has lower accuracy and efficiency for fatigue life prediction.

The proposed Markov process embeds the actual maximum and minimum stresses by a continuous updating process for stress load history data. This is to reduce the large credible intervals and missing loading points used for fatigue life prediction. With the reduction and missing loading intervals, the accuracy of fatigue life prediction for the crankshaft was validated using the statistical correlation properties.

It was observed that fatigue reliability corresponded well by reporting the accuracy of 95–98 per cent with a mean squared error of 1.5–3 per cent for durability and mean cycle to failure. Hence, the proposed fatigue reliability assessment provides an accurate, efficient, fast and cost-effective durability analysis in contrast to costly and lengthy experimental techniques.

An important implication of this study is durability-based life cycle assessment by developing the reliability and hazard rate index under random stress loading using the stochastic technique in modeling for improving the sensitivity of the strain gauge.

The durability analysis is one of the fundamental attributes for the safe operation of any component, especially in the automotive industry. Focusing on safety, structural health monitoring aims at the quantification of the probability of failure under mixed mode loading. In practice, diverse types of protective barriers are placed as safeguards from the hazard posed by the system operation.

Durability analysis has the ability to deal with the longevity and dependability of parts, products and systems in any industry. More poignantly, it is about controlling risk whereby engineering incorporates a wide variety of analytical techniques designed to help engineers understand the failure modes and patterns of these parts, products and systems. This would enable the automotive industry to improve design and increase the life cycle with the durability assessment field focussing on product reliability and sustainability assurance.

The accuracy of the simulated fatigue life was statistically correlated with a 95 per cent boundary condition towards the actual fatigue through the validation process using finite element analysis. Furthermore, the embedded Markov process has high accuracy in generating synthetic load history for the fatigue life cycle assessment. More importantly, the fatigue reliability life cycle assessment can be performed with high accuracy and efficiency in assessing the integrity of the component regarding structural integrity.