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.     

Fatigue of hybrid composites by a cohesive micromechanic model

A cohesive micromechanic fatigue model (CMFM) which identifies a nonconservative bonding reaction between a broken molecular chain and its neighbor as the main microscale source of fatigue damage accumulation has been recently developed for a unidirectional material constructed from a parallel set of chain-like elements. The successive breakages in each cycle are controlled by the statistical strength distribution of the elements and the probability and amount of interference which a broken element causes to its neighbors. The model gave a physically sound explanation to the fatigue power law S—N curve and the endurance limit phenomena by direct interpretations of microstructure parameters.

In this study the model is expanded by considering a material which have two components with different mechanical and statistical properties and are mixed to give a hybrid composite. The main target is to find the best combination for fatigue resistance, or more specifically, to explore the possibility of making a composite which is more fatigue resistant than each of its two components. It is found that mixing a brittle component (high modulus and low failure strain) with a soft one (low modulus and high failure strain) having a specific microstructure gives the desired effect if some requirements on the structural and mechanical properties are met.

The two materials are mixed in a form of bundles, so that the composite microstructure and fatigue resistance are controlled by their relative volume faction (a macro property) as well as the number of elements in each bundle (a micro property).     

Fatigue limit estimated using finite lives

For metallic material one is interested in estimating the fatigue limit although it is impossible to test if a specimen has infinite life. In this paper two models are compared. One model estimates the fatigue limit and another estimates the endurance limit. The model which estimates the endurance limit is a model which only uses the information that a specimen has broken or not broken at a certain stress level. The model which estimates the fatigue limit also uses the information about when the specimen is broken, i.e., after how many cycles the specimen breaks. The two models are compared, both on real and simulated staircase tests. It is shown that it is possible to estimate the distribution of the fatigue limit although the fatigue limit itself is impossible to observe. When the two models give very different estimates it indicates that the chosen run‐out level is too low.     

Modelling of fatigue damage progression and life of CFRP laminates

A progressive fatigue damage model has been developed for predicting damage accumulation and life of carbon fibre‐reinforced plastics (CFRP) laminates with arbitrary geometry and stacking sequence subjected to constant amplitude cyclic loading. The model comprises the components of stress analysis, fatigue failure analysis and fatigue material property degradation. Stress analysis of the composite laminate was performed by creating a three‐dimensional finite element model in the ANSYS FE code. Fatigue failure analysis was performed by using a set of Hashin‐type failure criteria and the Ye‐delamination criterion. Two types of material property degradations on the basis of element stiffness and strength were applied: a sudden degradation because of sudden failure detected by the fatigue failure criteria and a gradual degradation because of the nature of cyclic loading, which is driven by the increased number of cycles. The gradual degradation of the composite material was modelled by using functions relating the residual stiffness and residual strength of the laminate to the number of cycles. All model components have been programmed in the ANSYS FE code in order to create a user‐friendly macro‐routine. The model has been applied in two different quasi‐isotropic CFRP laminates subjected to tension–compression (T–C) fatigue and the predictions of fatigue life and damage accumulation as a function of the number of cycles were compared with experimental data available in the literature. A very good agreement was obtained.     

金属板材屈服行为与塑性失稳力学模型在微尺度下的应用

板材屈服准则与塑性失稳模型是精准描述高性能构件成形或服役过程的基础与前提。在板材塑性成形过程中,试样几何尺寸、材料晶粒大小、自由表面粗化和织构分布等都会对材料的塑性变形行为产生不可忽略的影响,导致单一尺度下的本构模型和断裂准则不能有效预测微观尺度下的材料变形行为和各种缺陷,大大限制了合金板材在航空、航天、汽车、医疗等工业上的应用。对现有屈服准则的研究进展进行了较为全面的回顾,从Hill、Hershey-Hosford和Drucker这3个系列出发,分别进行了对比分析,并总结了目前国内外用于验证屈服准则的金属板材双向拉伸实验机发展状况。基于不同的破裂失稳机理,将失稳模型分为宏观失稳准则、韧性断裂准则和耦合材料损伤演化的韧性断裂准则,并分别进行了归纳和阐述。此外,随着微成形技术的逐步推广,也对宏观塑性成形理论在微尺度下的应用进展进行了说明,指出了宏观屈服准则和失稳模型在微尺度下的不足和缺陷。最后讨论了宏观屈服准则和失稳模型今后的发展趋势以及宏观塑性成形理论在微尺度下的应用前景。     

Bounds on fatigue damage: relation to microstructure dependent crack growth: I. Constant amplitude cyclic damage

The paper attempts to account for the complex micro-processes at a crack tip through a phenomenological model of damage accumulation based on macro damage curves. With the S-N curve as a basis, bounds are established that bracket the mean cyclic damage in reversed constant amplitude cycling. Proceeding from single slip and opening mode damage curves, two-mode damage curves are derived that reflect the micro process of crack tip advance by the presence on a macro scale of both damage modes in each cycle. Discrete microstructure barriers are identified that help divide the fatigue process on a macro scale into three stages, the analogues of the three creep stages under constant stress whereby the microstructure short crack (MSC), physically small crack (PSC) and macro crack regimes correspond to the `primary', `steady' and `tertiary' creep macro stages. The fatigue process is found to consist at each cyclic load level of a macro slip stage followed by an opening mode stage with an abrupt damage rate change at the transition, in line with experimental evidence (Socie, 1993). The barriers divide the entire region behind the S-N curve into distinct cyclic strain (stress) domains dominated on a macro scale by the opening mode in regions nearest the fatigue limit and by the slip mode in the uppermost region while an intermediate region is dominated by both. In the region nearest the fatigue limit the opening mode dominates virtually from first load reversal, in line with a view (Miller, 1985, 1987) that relates damage to surface imperfections. Macro damage accumulation involving a discontinuous damage rate transition is treated on the basis of discrete barriers while a continuous spectrum of barriers is introduced in an attempt to reflect the crack tip process on a macro scale. A theoretical model of microstructure resistance is introduced that describes crack arrest by the barriers and leads to a distinct set of macro-damage bounds in the interval between barriers, hence in each region of the S-N curve. The entire range of fatigue lifetimes below and above the fatigue limit is examined showing that only the slip mode carries over to the region below the fatigue limit resulting in non-propagating damage. Assuming that macro damage can be defined as a ratio of crack lengths, two scales are introduced that lead to bounds on mean crack length: a macro scale connecting two disparate levels of the fatigue process defines a macro volume element enclosing a sufficiently large number of grains to be representative of the actual medium as a whole and a micro scale of grain size order with a corresponding role. Bounds on mean crack growth rate are found to reduce in the limit of long cracks to the known Paris rate relation. Two distinct sets of bounds on mean damage and damage rate are found: one for unloading from a high to low cyclic strain another for loading from a low to high strain (stress), congruent with the distinct loading/unloading paths in a hysteresis loop. A simple test method is proposed to locate the fatigue limit indirectly. The model is applied to cumulative damage analysis in part II where residual lifetime mean and variance in two-stage fatigue cycling are predicted.     

Reliability of reinforced concrete structures under fatigue

This paper focuses on time-variant reliability assessment of deteriorating reinforced concrete structures under fatigue conditions. A strategy combining two time scales, namely the micro-scale of instantaneous structural dynamics (or statics) and the macro-scale of structural lifetime, is proposed. Non-linear response of reinforced concrete structures is simulated by means of the finite element method with adequate material model. A phenomenological fatigue damage model of reinforced concrete is developed and calibrated against experimental results available in the literature. Reliability estimates are obtained within the response surface method using the importance/adaptive sampling techniques and the time-integrated approach. The proposed assessment strategy is illustrated by an example of a concrete arch under fatigue loading. The obtained results show a general inapplicability of local and linear fatigue models to system level of structures.     

Hierarchical multiscale modeling of failure in unidirectional fiber-reinforced plastic matrix composite

A hierarchical multiscale approach is applied to study the tensile strength of fiber-reinforced composites. The approach is carried out in three scales: micro, meso and macro-scales, which are linked by information transfer from small to large-scale. In micro-scale, a 3D column model was established to calculate the residual stresses, which is fed into mesoscale for interfacial friction stress; in mesoscale, a representative volume (RVE) with a central broken fiber and four neighbor fibers is modeled, where matrix plastic hardening is considered. Local stress distribution in RVE is simulated by shear-lag model, and transferred into macro-scale for progressive damage simulation. In macro-scale, Monte Carlo simulations with the present shear-lag model were then conducted to obtain the ultimate tensile strength. Through this hierarchical multiscale simulation, composite macro-performance can be predicted by micro-scale parameters, this relationship will give a reference for composite design and optimization.     

锻锤基础的冲击疲劳损伤分析

用损伤力学的概念提出了一种研究由锻锤锻打引起锻锤基础系统的疲劳损伤增长和疲劳寿命估计的方法。该方法通过定义,引入锻锤基础系统中减振垫与基础块的损伤状态寿命因子,能够估计出锻锤基础系统的减振垫和基础块的损伤疲劳寿命上、下限。通过分析发现,长期的重复冲击载荷会引起锻锤基础系统发生疲劳微损伤积累,疲劳损伤积累的宏观损伤又引起锻锤基础的动力响应随宏观损伤发展而增大,动力响应的增大又加剧基础系统的损伤发展。因此,为减少周围环境的振动以及保护周围环境免受锻锤冲击损伤,在锻锤基础系统设计中需考虑吸振和损伤控制。     

Fatigue damage of low amplitude cycles in low carbon steel

The influences of low load cycles on fatigue damage in 0.15% C steel (C15E, No. 1.1141) are investigated in the very high cycle fatigue regime using ultrasonic fatigue testing equipment. Constant amplitude (CA) endurance limits at limiting lifetime of 10⁹ cycles are determined in cyclic tension–compression and cyclic torsion tests. Non-propagating fatigue cracks are found in specimens subjected to cyclic torsion loading at the endurance limit. The endurance limit is considered as maximum stress amplitude where possibly initiated fatigue cracks do not propagate to failure. Two-step variable amplitude (VA) tension–compression endurance tests are performed with repeat sequences consisting of high stress amplitudes above the endurance limit and far greater number of cycles below. The measured lifetimes are compared with linear damage accumulation calculations (Miner calculations). If the high stress amplitude is more than approximately 13% above the CA endurance limit, detrimental influences of low load cycles and failures at low damage sums are found. If the high stress is less than 13% above the CA endurance limit, numerous low load cycles cause prolonged fatigue lifetimes and specimens can sustain large damage sums without failure. Two-step VA fatigue crack growth investigations show that load cycles below the threshold stress intensity accelerate crack growth, if the high stress intensity is 18% or more above the CA threshold stress intensity. In repeat sequences with high stress intensities 14% above threshold stress intensity, low load cycles decelerated and stopped fatigue crack growth. Low load cycles can reduce or prolong fatigue lifetimes of low carbon steel and one reason is the accelerated or retarded fatigue crack growth due to numerous low amplitudes, and the maximum load amplitude of a VA load sequence determines whether detrimental or beneficial effects prevail.     

金属材料低温疲劳性能的预测方法

本文总结了作者近来研究金属低温疲劳取得的进展,主要内容包括:疲劳极限的热激活模型、应变疲劳公式、疲劳始裂寿命和裂纹扩展速率的定量预测方法、疲劳裂纹扩展机制脆转模型。当室温下的疲劳极限和门槛植ΔK_(th)确定后,应用本文的方法可根据拉伸性能定量预测材料在低温下的疲劳极限、应变疲劳寿命、疲劳始裂寿命和裂纹扩展速率,并且不需要低温疲劳试验和经验修正。     

Beitrag niedriger Lastamplituden zur Ermüdungsschädigung von 0,15 %C Stahl

Contribution of low load cycles to fatigue damage in 0.15 %C steel The S‐N curve of 0.15 %C steel shows an endurance limit. Two‐step variable amplitude loading experiments serve to investigate the influence of numerous cycles below the endurance limit on fatigue damage. If high stress amplitudes of the loading sequences are more than approx. 15 % above the endurance limit, low load cycles contribute significantly to fatigue damage. Investigations of fatigue crack propagation under two‐step variable amplitude loading show accelerated crack growth caused by low load cycles. If high stress amplitudes of the two‐step sequences are less than 15 % above the endurance limit, beneficial influences of numerous low load cycles are found. Under these conditions, the material can sustain far greater numbers of load cycles than predicted by Miner damage accumulation calculation. Fatigue crack growth studies show that under these conditions for the high load numerous low load cycles lead to stop of the crack propagation.     

Accelerated fatigue testing method

A method for accelerated fatigue testing of materials, based on a cumulative damage rule, is developed and examined. The method is based on monotonically increasing the stress amplitude with the number of cycles, until failure. When the initial stress amplitude is above the endurance limit, two tests are needed to determine the S/N curve; another test, with an initial stress amplitude below the endurance limit, is needed to determine the fatigue endurance limit. It is shown how to choose the right loading rate and starting level. This method minimizes the number of tests needed for the determination of the fatigue strength endurance limit, and also shortens these tests by reducing the number of cycles, (as each test ends with specimen failure).     

Tension-tension fatigue of a cross-woven C/SiC composite

The tension-tension fatigue behavior of a cross woven C/SiC composite was studied in terms of damage modes and damage development. The fatigue stress versus life diagram (S-N) curve and an endurance limit of 320–340 MPa (about 80% tensile UTS) for 10⁶ cycles were obtained for the C/SiC composite. Different fatigue behaviors were found for samples that failed during fatigue and for samples that survived 10⁶ cycles. Seven fatigue damage modes were observed, the development of which were used to explain the different fatigue behaviors. For the fatigue-failed samples, the degrees of damage of the seven modes increased with increase of cycles, leading to an increase in elapsed strain and a decrease in composite modulus. For fatigue-survived samples, the development of all the damage modes except for fiber breaking caused an initial increase of elapsed strain and decrease of composite modulus, but at high cycles, fiber bundle realignment and straightening in these samples led to partial recovery of the modulus and cessation of the damage development.     

Entwicklung auf dem Gebiet der Lebensdauervorhersage an mehrachsig beanspruchten komplexen Bauteilen

Developments of Fatigue Life Prediction Methods for Components with Multiaxial Stress States For further reductions of the structural weight of modern light weight constructions the explicit consideration of multiaxial stress states becomes increasingly important. In the present paper a survey of prediction methods for the evaluation of the life behaviour close to the endurance limit and in the finite life range is given. A main characteristic of the prediction methods especially for the limited life range is that individual stress-strain events similar to closed hysteresis loops under uniaxial constant amplitude conditions have to be present. In order to overcome this limitation, a new fatigue life evaluation procedure has been developed. The prediction method is based on a threedimensional elastic-plastic finite element model together with the material model after Mróz to account for the elasticplastic material behaviour. The fatigue damage is evaluated on the basis of plastic work using a new incremental damage law. The new method is briefly described.     

Dislocation evolution in interstitial-free steel during fatigue near the endurance limit

In order to clear the relationship between dislocation development and endurance limit in fatigued body-centered cubic (BCC) metals, the automotive grade interstitial-free steel (IF steel) was fatigued near the endurance limit in this study. When cycling just below the endurance limit, the dislocation structures are mainly composed of loop patches, moreover, a few large dislocation cells and dislocation walls can also be found, and thus these structures have no significant effect on fatigue failure. However, once cyclic strain slightly exceeds the endurance limit, the small dislocation cells tend to develop near grain boundaries and triple junction of the grains, and which provide a more appropriate structure for crack growth than do large dislocation cells.     

FATIGUE-MICROSTRUCTURE RELATIONSHIPS IN SOME AGED ALUMINIUM ALLOYS

Abstract Aluminium–copper–magnesium alloys show a high response to age hardening but have relatively poor fatigue properties, whereas the reverse is true for aluminium magnesium alloys. Small additions of silver (∼0.1 atomic %) change both the type and dispersion of precipitates in Al–Cu–Mg alloys and promote age hardening in Al–Mg alloys in which it is normally absent. The paper is concerned with the effects of silver on the behaviour of representative Al–Cu–Mg and Al–Mg alloys tested under fatigue conditions.
Despite the fact that silver increases the response to age hardening in Al–Cu–Mg alloys, the fatigue endurance limit is reduced. This effect is even more marked with the alloy Al–5% Mg in which the 0.2% proof stress was increased from 85 to 200 MPa by adding silver, whereas the fatigue endurance limit fell from ±87 to ±48 MPa. In both systems, silver promotes formation of finely dispersed precipitates, and the poor fatigue properties are associated with the concentration of dislocations in intense slip bands. On the other hand, when large precipitate particles are present, dislocations are more uniformly dispersed and the fatigue properties are improved.