A plausible strategy for modeling fatigue life variation

In this paper stochastic modeling is used to predict fatigue life uncertainty by simulating small variations in strain-life material constants. The Monte Carlo method,^[1] using either known cumulative distribution functions (CDFs) for the material constants and/or postulated CDFs, provides the mechanism to generate a set of failure data. These data are analyzed, using ordinary statistical techniques, to develop the Weibull CDF for cycles to failure. It is seen that small variations (∼±15%) in values of the strain-life constants result in large variations (∼600%) in predicted fatigue life at moderate strain. The often-observed phenomenon that spread in fatigue data is greater at lower strain is also described by the stochastic model.     

The cyclic strain resistance, fatigue life and final fracture behavior of magnesium alloys

This paper summarizes the results of a comprehensive study on the cyclic strain resistance, low-cycle fatigue life and fracture behavior of three rapidly solidification processed magnesium alloys. Test specimens of the magnesium alloy were cyclically deformed under fully-reversed total strain amplitude control straining, over a range of strain amplitudes, giving less than 10⁴ cycles to failure. The cyclic stress response characteristics, strain resistance and low-cycle fatigue life of the alloys are discussed in light of alloy composition. All three alloys follow the Basquin and Coffin-Manson strain relationships, and exhibit a single slope for the variation of cyclic elastic and cyclic plastic strain amplitude with reversals-to-fatigue failure. The cyclic stress response characteristics, fatigue life and final fracture behavior of the alloy are discussed in light of competing and synergistic influences of cyclic total strain amplitude, response stress, intrinsic microstructural effects and dislocation-microstructural feature interactions during fully-reserved strain cycling.     

The needs of understanding stochastic fatigue failure for the automobile crankshaft: A review

This paper reviews the fatigue failure mechanisms for the automobile crankshaft under service loading through the stochastic point of view. Fatigue failure of crankshafts are reviewed in general, as it is a major concern due to the uncertainties that arise i.e. randomness in structural materials, the geometric shape of the component and randomness of service loads. There has been very little research carried out in assessing the fatigue failure using the stochastic process in predicting the fatigue life of crankshafts. This review paper discusses the durability aspects of the component and is followed by a review of the characteristics of loading and the stochastic fatigue failure effect on the components. In addition, the stochastic approach from empirical model aspect using a safe-life approach from the more recent advances in computational methods to assess stochastic fatigue failure was discussed and reviewed in the context of this paper. The integration between the empirical and probabilistic methods can be quantified using statistical models, which evaluate the damage that leads to fatigue and eventually fatigue failure. Hence, this review provides a platform for understanding the stochastic fatigue failure for an accurate predictive prediction on the structural integrity of components, especially in the automobile industry.     

Curvilinear fatigue crack reliability analysis by stochastic boundary element method

In this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first-order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non-linearity of the response, direct differentiation coupied with the response-surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first-order response model. An iteration scheme based on the HL-RF method² is applied to locate the most probable failure point on the limit-state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.     

一个新的低周疲劳失效准则

利用修正的塑怀循环应变能记响应数学模型，给出了一个新的低周疲劳失效准则，由此得出了低周疲劳寿命的估算公式，并且采用低周疲劳试验验证该失效准则的合理性和有效性。     

Random fatigue crack growth in mixed mode by stochastic collocation method

Fatigue crack growth is uncertain, either for cracking rate or direction. The stochastic models proposed in the literature suffer from limited applicability or lack of physical meaning. In this paper, a new stochastic collocation method is proposed to solve mixed mode fatigue crack growth problems with uncertain parameters. This approach has the advantage of non-intrusive nature methods, such as Monte-Carlo simulations, since it allows us to decouple the stochastic and the mechanical computations. The proposed numerical implementation is very simple, as it requires only repetitive runs of deterministic finite element analysis at some specific points in the random space. The method describes a precise approximation of the mechanical response corresponding to the fatigue life, in order to assess the stochastic properties, namely the statistical moments and the probability density function of fatigue life. The performance of the stochastic collocation method for dealing with this kind of problems has been evaluated through two numerical examples, showing the high performance for practical applications. Moreover, the proposed method is extended in the last example to the failure probability assessment, with respect to the target service life.     

On the failure condition in strain-controlled low cycle fatigue

Axial-strain controlled low cycle fatigue tests were performed on several materials in different metallurgical conditions using various test-piece geometries, strain ranges, temperatures and frequencies in order to arrive at a proper choice for the definition of failure. Several alternative failure criteria proposed in the literature were examined in terms of load response measurements and the shape of the hysteresis loop in the compressive portion of the cycle. A 20% fall in the saturation stress in tension and cusp formation in the compressive portion of the cycle have been identified as the two best criteria for defining the failure life of laboratory specimens in strain-controlled low cycle fatigue testing.     

Fatigue failure in graphite fibre and glass fibre-polymer composites

Our studies have established that unidirectional graphite fibre composites show excellent fatigue resistance with only a 20 to 30% decrease in strength with cycling. Fatigue failures invariably occurred on the surfaces undergoing compression and were identified by scanning electron microscope studies as resulting from matrix failure adjacent to local fibre buckling failure zones. In contrast, glass fibre composites showed a much larger (70%) loss in strength under cyclic loading. At intermediate lives, failure occurred by the growth of matrix microcracks followed by delamination, while at long lives, the applied stress levels were below the microcrack initiation stress and behaviour was characterized by crack nucleation processes. These results have suggested a criterion for predicting high cycle fatigue strength which is based on the hypothesis that for failure to occur, the maximum applied effective cyclic strain in the composite must exceed a critical value which depends upon the fatigue response of the matrix material. The main assumption is that localized fatigue failures in the matrix are the predominant contributions to the ultimate fatigue failure of the composite.     

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

There are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out-of-phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in-phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.     

A cohesive micromechanic fatigue model. Part II: Fatigue-creep interaction and Goodman diagram

A Cohesive Micromechanic Fatigue Model (CMFM), which identifies a chemical reaction between a broken chain and its neighbor as the main micro-scale source of fatigue failure has been developed recently. The successive chain breakages which control the damage evolution were characterized by the statistical strength distribution of the chains and the probability of the neighbor to break. The model explained the power law S-N curve for high cycle fatigue and the endurance limit phenomenon.

In this study, the basic concept is expanded by defining two kinds of breakage sources for the neighbors. A dynamic type, associated with the local transient disturbance, occurring during breakage, and a static type, related to the relative motion between adjacent chains. The first is dominated by the strain at the breaking point and leads to a creep like macro response. The second is a function of the maximum strain difference experienced during unloading, which causes fatigue failure.

The interaction between the two mechanisms gives a total macro response which depends on both the mean and the alternate stress. Results provide a theoretical explanation to the empirical “Goodman diagram” and to the low cycle fatigue behavior. The effect of different probability functions for the chemical reaction was studied. An activation type was found most suitable for predicting the macro response, and a Weibull distribution has been used. All material parameters which were introduced on the microscale, have a direct, uncoupled outcome on the macro response.     

MEAN STRESS EFFECTS ON LOW CYCLE FATIGUE FOR A HIGH STRENGTH STEEL

Abstract— ASTM A723 Q & T steel with a yield strength and ultimate strength of 1170 and 1262 MPa respectively was evaluated for mean stress-strain effects under smooth specimen axial strain controlled low cycle fatigue conditions with strain ratios R of −2, −1, 0, 0.5 and 0.75. Cycles to failure ranged from 15 to 10⁵. Cyclic stress-strain response based upon half-life hysteresis loop peaks were similar for all R ratios. Mean stress relaxation occurred for R ≠−1 only when plastic strain amplitudes were present and this occurred above total strain amplitudes of 0.005. Thus, mean stress relaxation was completely dependent upon cyclic plasticity. Mean strains did not affect low cycle fatigue life unless accompanied by half-life mean stress. Tensile mean stress was detrimental and compressive mean stress was beneficial and these effects only occurred at strain ampltidues below 0.005. Three different mean stress models were used to evaluate the low cycle fatigue data and the SWT log-log linear model best represented the data. These results can be used with the local notch strain fatigue life prediction methodology.     

A comparative study of failure criteria in probabilistic fields and stochastic failure envelopes of composite materials

One of the major objectives of this paper is to offer a practical tool for materials design of unidirectional composite laminates under in-plane multiaxial load. Design-oriented failure criteria of composite materials are applied to construct the evaluation model of probabilistic safety based on the extended structural reliability theory. Typical failure criteria such as maximum stress, maximum strain and quadratic polynomial failure criteria are compared from the viewpoint of reliability-oriented materials design of composite materials. The new design diagram which shows the feasible region on in-plane strain space and corresponds to safety index or failure probability is also proposed. These stochastic failure envelope diagrams which are drawn in in-plane strain space enable one to evaluate the stochastic behavior of a composite laminate with any lamination angle under multi-axial stress or strain condition. Numerical analysis for a graphite/epoxy laminate of T300/5208 is shown for the comparative verification of failure criteria under the various combinations of multi-axial load conditions and lamination angles. The stochastic failure envelopes of T300/5208 were also described in in-plane strain space.     

Low cycle fatigue behaviour of particulate reinforced metal matrix composites

The low cycle fatigue (LCF) resistance of two different 6061 Al/20 vol% alumina particulate metal matrix composites (MMCs) in a peaked-aged condition has been evaluated under fully reversed strain control testing. Test results were combined with scanning electron and optical microscopy investigations to determine the effects of reinforcement particles and strain amplitude on the LCF behaviour of these MMCs. Both materials show three stages of response to LCF: initial fast hardening or softening in the first few cycles; gradual softening for most of the fatigue life; and a rapid drop in the stress carrying capability prior to failure. Both MMCs exhibit short LCF life which follows a Coffin-Manson relationship. All tested specimens demonstrate ductile fracture morphology at final failure. The experimental results are discussed in respect of strain amplitude, matrix composition and reinforcement shape and crack initiation.     

Notch effect on creep–fatigue life for Sn–3.5Ag solder

This paper studies the creep–fatigue crack initiation and failure lives of Sn–3.5Ag solder notched specimens focused on the multiaxial strain at the notch root. Push–pull creep–fatigue tests were performed using three circumferential notched specimens using four kinds of creep–fatigue strain waveforms. Multiaxial strains at the notched section were calculated by finite element (FE) analysis under four kinds of creep–fatigue loading. Creep–fatigue damage laws were applied for evaluating the crack initiation and failure lives using the multiaxial strains obtained by the FE analysis. von Mises equivalent strain at the notch root estimated the crack initiation lives with a large scatter as well as the failure lives. Instead, the mean value of von Mises equivalent strain over the cross section of the notch root estimated the crack initiation and failure lives with a small scatter.     

Multi‐scale experimental study on fatigue damage behaviour and its effect on structural nonlinear response

Experimental analyses on the structural response caused by local fatigue damage accumulation in welded details are accomplished to perform failure process and nonlinear effect analysis at different structural levels. The experiment is carried out by using welded compact tension (CT) specimens and a scaled truss specimen, and all of them have a notch at the weld toe to facilitate damage initiation. Cyclic loads are applied to those specimens to generate accumulative fatigue damage, respectively. The process of fatigue accumulation including initiation and propagation of fatigue cracks in the welded detail and resultant structural responses of CT specimens and the truss are measured with integration of multiple testing techniques. Multi‐scale experimental results show that microscopic‐/mesoscopic‐concentrated strain and extension of plastic zone in the vicinity of notch tip are both affected significantly by the fatigue damage accumulation and present appreciable nonlinear behaviour; however, the macroscopic response such as the frequency and stiffness parameters of the welded truss specimen are less sensitive to the low‐level fatigue damage. It is concluded that the fatigue failure of the welded truss is a multi‐scale progressive process due to fatigue damage trans‐scale evolving, in which the local meso‐damage firstly affects local strain of plastic zone in the vicinity of the notch tip, and then fatigue damage evolving from meso‐ to macro‐scale affects nonlinear responses of the damaged components; lastly, the fatigue failure could be expected as the results of the propagation of macroscopic fatigue cracks.     

Effects of microstructure on the strain-controlled fatigue failure behavior of an aluminium-alloy/ceramic-particle composite

A study has been made to understand the cyclic fatigue and cyclic fracture characteristics of a cast aluminium alloy metal matrix discontinuously reinforced with particulate silicon carbide. The Al/SiC_p composite was strained to failure over a range of strain amplitudes giving lives of less than 10⁴ cycles to failure. The specimens were cycled by using tension-compression loading under total strain control. In the as-cast condition, the aluminum-alloy/ceramic composite displayed combinations of cyclic hardening and softening to failure at higher cyclic-strain amplitudes, and progressive softening to failure at low cyclic-strain amplitudes. The spray-atomized and deposited composite exhibited softening to failure at the higher cyclic-strain amplitudes and combinations of softening and hardening behavior at the lower strain amplitudes. The observed hardening and softening behavior is a mechanical effect and attributed to concurrent and competing influences of interactions between cyclic deformation and composite microstructure during cyclic straining. The processed microstructure exhibited better cyclic ductility and cyclic-strain resistance than the as-cast composite microstructure. The cyclic fatigue behavior of the alloy is briefly interpreted in the light of composite microstructural effects, plastic strain amplitude and concomitant response stress.     

Influence of temperature on the low cycle fatigue behaviour of a modified 9Cr–1Mo ferritic steel

Low cycle fatigue (LCF) behaviour of a modified 9Cr–1Mo steel under normalized and tempered conditions is reported. The alloy was normalized at 1313K for 1 h followed by tempering at 1033K for 1 h, which resulted in a tempered martensitic structure. Total axial strain controlled LCF tests were conducted at a constant strain rate of 3×10⁻³ s⁻¹ at different strain amplitudes varying from ±0.25 to ±1.0% in the temperature range of 300–873K. The cyclic stress response behaviour, in general, showed an initial brief hardening for the first few cycles, followed by a continuous and gradual softening regime that ended in a stress plateau that continued up to the specimen failure. The fatigue life decreased as the temperature increased. The temperature effect on life was more pronounced at low strain amplitudes. The metallography of the failed samples revealed that the fatigue failure at high amplitudes of testing was marked by extensive crack branching and the formation of secondary cracks. Oxidation was found to exert major influence on LCF life reduction at 873K.     

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

Low cycle fatigue and fracture behaviour of cast Cu–Pb alloys

Abstract

The influence of alloy composition on cyclic stress response, cyclic strain resistance, and cyclic fracture behaviour is reported. Three Cu–Pb alloys containing 10, 25, or 40 wt-%Pb were investigated. Alloy composition, i.e. lead content, was observed to have an influence on cyclic stress response, cyclic ductility, and low cycle fatigue life. The cyclic stress response characteristics, fatigue life, and failure process are discussed in the light of the specific roles played by concurrent and mutually interactive influences of plastic strain amplitude, concomitant response stress, and intrinsic microstructural effects.

MST/1918     

Effects of intermittent loading time and stress ratio on dwell fatigue behavior of titanium alloy Ti-6Al-4V ELI used in deep-sea submersibles

Different components of deep-sea submersibles,such as the pressure hull,are usually subjected to inter-mittent loading,dwell loading,and unloading during service.Therefore,for the design and reliability assessment of structural parts under dwell fatigue loading,understanding the effects of intermittent loading time on dwell fatigue behavior of the alloys is essential.In this study,the effects of the inter-mittent loading time and stress ratio on dwell fatigue behavior of the titanium alloy Ti-6Al-4V ELI were investigated.Results suggest that the dwell fatigue failure modes of Ti-6Al-4V ELI can be classified into three types,i.e.,fatigue failure mode,ductile failure mode,and mixed failure mode.The intermittent loading time does not affect the dwell fatigue behavior,whereas the stress ratio significantly affects the dwell fatigue life and dwell fatigue mechanism.The dwell fatigue life increases with an increase in the stress ratio for the same maximum stress,and specimens with a negative stress ratio tend to undergo ductile failure.The mechanism of dwell fatigue of titanium alloys is attribute to an increase in the plastic strain caused by the part of the dwell loading,thereby resulting in an increase in the actual stress of the specimens during the subsequent loading cycles and aiding the growth of the formed crack or damage,along with the local plastic strain or damage induced by the part of the fatigue load promoting the cumu-lative plastic strain during the dwell fatigue process.The interaction between dwell loading and fatigue loading accelerates specimen failure,in contrast to the case for individual creep or fatigue loading alone.The dwell fatigue life and cumulative maximum strain during the first loading cycle could be correlated by a linear relationship on the log-log scale.This relationship can be used to evaluate the dwell fatigue life of Ti alloys with the maximum stress dwell.