A Continuum Mechanics Approach for Crack Initiation and Crack Growth Predictions

Very often, different approaches are used for crack initiation and crack growth predictions. The current article introduces a recently developed approach that can be used for the predictions of both crack initiation and crack propagation. A basic assumption is that both crack nucleation and crack growth are governed by the same fatigue damage mechanisms and a single fatigue damage criterion can model both stages. A rule is that any material point fails to form a fresh crack if the total accumulated fatigue damage reaches a limit. For crack initiation predictions, the stresses and strains are obtained either directly from experiments or though a numerical analysis. For the prediction of crack growth, the approach consists of two steps. Elastic‐plastic stress analysis is conducted to obtain the detailed stress‐strain responses. A general fatigue criterion is used to predict fatigue crack growth. Compact specimens made of 1070 steel were experimentally tested under constant amplitude loading with different R‐ratios and the overloading influence. The capability of the approach to predict both crack initiation and the crack growth under these loading conditions was demonstrated by comparing the predictions with the experimental observations.     

Prediction of fretting fatigue crack initiation in double lap bolted joint using Continuum Damage Mechanics

In fretting fatigue, the combination of small oscillatory motion, normal pressure and cyclic axial loading develops a noticeable stress concentration at the contact zone leading to accumulation of damage in fretted region, which produces micro cracks, and consequently forms a leading crack that can lead to failure. In fretting fatigue experiments, it is very difficult to detect the crack initiation phase. Damages and cracks are always hidden between the counterpart surfaces. Therefore, numerical modeling techniques for analyzing fretting fatigue crack initiation provide a precious tool to study this phenomenon. This article gives an insight in fretting fatigue crack initiation. This is done by means of an experimental set up and numerical models developed with the Finite Element Analysis (FEA) software package ABAQUS. Using Continuum Damage Mechanics (CDM) approach in conjunction with FEA, an uncoupled damage evolution law is used to model fretting fatigue crack initiation lifetime of Double Bolted Lap Joint (DBLJ). The predicted fatigue lifetimes are in good agreement with the experimentally measured ones. This comparison provides insight to the contribution of damage initiation and crack propagation in the total fatigue lifetime of DBLJ test specimens.     

Fatigue life prediction: A Continuum Damage Mechanics and Fracture Mechanics approach

Continuum Damage Mechanics (CDM) approach is used to predict crack initiation life and Fracture Mechanics approach predicts crack growth life. Strain controlled fatigue life of a ferrous alloy, EN 19 steel, has been determined using CDM and Fracture Mechanics approach. By combining these two approaches, life could be predicted with damage value in the material. All inputs required for the models have been determined by conducting monotonic, cyclic and fracture tests. Predicted life is also compared by conducting strain controlled fatigue tests. Predicted life in the strain amplitude range of 0.3–0.7% (fatigue life range of 10²–10⁵), compares well with the experimental results. All tests have been conducted at specimen level, stress ratio of −1 and at room temperature. The variation of crack initiation and crack propagation life with strain amplitude shows that maximum life is consumed by crack growth process at higher strain amplitude and at lower strain amplitudes, maximum life is spent for crack initiation process.     

On the Relevance of Mean Field to Continuum Damage Mechanics

Damage theory is, by its very essence, a mean-field theory. In this note, we argue that considering the effective interaction kernel between an additional micro-crack, and the effective equivalent damaged matrix, the power-law decay of the influence function (or Green's function) becomes more and more long-ranged as the tangent modulus vanishes. Moreover, the reloaded region becomes a narrower and narrower `cone', so that the damage in this cone becomes closer and closer to the so-called global load sharing rule used, for instance, to study a fiber bundle. This constitutes a formal justification of the relevance of such a mean-field approach as the peak stress is approached.     

基于损伤力学的疲劳裂纹萌生及扩展规律研究

针对金属构件疲劳裂纹的萌生、扩展寿命及其规律等问题,应用损伤力学理论与有限元相结合的方法,建立了计算疲劳裂纹全寿命的统一模型。引入附加载荷法,通过MATLAB编程计算,实现了对刚度矩阵的连续计算,并给出了编程的流程。通过对单个单元的损伤计算,得到了单元从无损到破坏过程中等效应力的变化;通过计算各个构件损伤单元寿命,进而给出了金属构件总体疲劳寿命。分析得到了微裂纹萌生及扩展寿命占总体疲劳寿命的80%以上,并应用有限元软件ANSYS模拟给出了缺口件裂纹萌生及扩展过程。理论计算的结果与试验数据对比基本一致,验证了本工作方法的准确性。     

Creep failure of a simply supported beam through a uniaxial Continuum Damage Mechanics model

Summary Creep failure of elastic-damageable beams is investigated using a simple Continuum Damage Mechanics model. A single-degree-of-freedom system is first studied for the bending problem of the visco-damage spring. The strong analogy between the behavior of such a system and the one of an imperfection sensitive viscoelastic column, with specific references to the buckling of columns is shown. In particular, the saddle-node bifurcation is clearly recognized in the bifurcation diagram. Large displacement analysis is considered when the true collapse mode is studied. The continuous beam is then studied with a local damage constitutive law. It is shown that the evolution problem, composed of a loading range and the creep test, is well posed for this statically determinate beam. It appears that it is not necessary to introduce some non-locality in the constitutive law, in order to regularize the evolution problem. The stability analysis at the structural level leads to a similar conclusion. There is a limit point in the bifurcation diagram (which is a functional space for this continuous problem). This limit point is obtained via analytical arguments. The limit load depends on the geometrical and material characteristics of the problem but does not depend on the viscosity of the local constitutive law. Numerical simulations illustrate the collapse mode.     

An Evaluation of Linear Cumulative Damage (Miner's Law) Using Kinetic Crack Growth Theory

Taking a basis set of creep failure functions as specifying the failureproperties for a class of materials, various damage laws can be used topredict failure under any type of stress history. A particularlyconvenient form is that of Miner's law also known as Linear CumulativeDamage. However, such damage laws are entirely empirical and ofuncertain value. A kinetic crack growth theory developed for polymers isused to evaluate Linear Cumulative Damage. LCD is found to be generallyunsatisfactory. However, there is an important sub-class of cases whereit does perform well, and this can be of importance in an acceleratedtesting methodology for polymers.     

Creep Failure Simulation in 9%Cr Heat-Resistant Steel Joint Based on the Continuum Damage Mechanics

Strength of Materials - Creep failure in a typical 9%Cr steel joint (i.e., T92 welded joint) was simulated based on the continuum damage mechanics (CDM) with a modified Kachanov–Rabotnov...     

Identification of Damage and Plasticity Parameters for Continuum Damage Mechanics Modelling of Carbon and Glass Fibre‐Reinforced Composite Materials

Abstract: An experimental test series was carried out to determine input parameters for a well‐known continuum damage mechanics elementary ply plasticity model. A full suite of data was obtained for a carbon fibre and an S2‐glass fibre‐reinforced composite material, both currently used in the aerospace industry. Models were implemented using the experimentally determined input parameters and predictions for in‐plane behaviour found good agreement with experiments for both material systems. In addition, model predictions for cyclic loading accurately captured reload moduli and plastic strain magnitude.     

Simulation of Stable Crack Growth for Welded Joints Including Strength Mismatching

1.IotroductionStrengthmismatchingeffectsonfracturetough-nessofferritesteelsremainakeyissueforthesafetyassessmentofstructures.Structuralandpressureves-selsteelsgenerallyexhibitincreaseinfracturetough-nessoverthefirstfewdistanceofstablecrackgrowth.Laboratorytestingoffracturespecimenstomeasureresistancecurves(R-curves)consistentlyrevealsamarkedeffectofstrengthmismatchingonR-curves.Fortheweldedjoint,whoseweldmetalstrengthishigherthanthatofthebasemetal(overmatching),yieldahigherRcurvecomparingwit…     

Influence of small variations of initial defects upon crack paths in creeping plates – Continuum Damage Mechanics description

It has been shown in previous works by the authors that the entire process of failure of a structure can be described within the frame of Continuum Damage Mechanics (CDM). It consists of crack initiation, growth (including branching) and proliferation throughout a structure, which terminates structure’s lifetime. These characteristic periods are especially well exposed when time dependent behavior of the structure’s material (e.g. creep) is taken into account. The results of numerical simulation of the process depend, however, on a number of factors like assumed constitutive equations for material behavior, values of material constants, and boundary and initial conditions. Due to the nonlinear behavior typical for metals in high temperature applications, the solutions are very sensitive to these parameters. In particular, times to reach consecutive stages of failure process can vary considerably.In the present contribution the influence of initial distribution of damage variable, which can result from material original heterogeneity or can be artificially introduced, is studied. It is demonstrated that even a small variation in these conditions can influence crack paths and – consequently – the time to final failure of a structure, which can be very different from that when zero-value initial conditions are superimposed upon damage scalar parameter.     

蠕变裂纹启裂和扩展的局部损伤理论

根据局部损伤理论和相似原理，给出了蠕谱裂纹启列前的孕育上下限时间并推导了蠕变裂纹扩展率方程。在常载荷下用２．２５Ｃｒ－１Ｍｏ钢作了蠕变裂纹扩展试验，高拘束度使早期局部损伤发展迅速，实验结果与孕育时间下限接近。稳态预测值由于忽略未开裂部分材质劣化而略氏于实验结果值。有限元模拟损伤演变过程。表明稳态裂纹扩展民实验结果吻合。     

用损伤变量D2作为裂纹扩展阶段强度与寿命的计算参量

就多晶体弹塑性材料在疲劳载荷作用下从宏观裂纹的形成、扩展直至断裂的裂纹扩展阶段,提出了用损伤变量D2作为本阶段强度与寿命的计算参量,提出了这个过程描述材料疲劳断裂行为的新方程,并使这些方程与现有广泛应用的其他方程相互沟通,从而对某些材料行为的变化规律形成一个整体的认识,以便于工程界能广泛地理解、接受和应用.     

一个新的超塑变形内部损伤预测模型

超塑变形往往具有空洞敏感性，对空洞的研究引起国内外学者的重视并取得较大进展，但现有描述超塑变形时空洞损伤行为的力学模型普遍存在精度问题，利用神经网络对超塑变形时的空洞损伤程度进行预测，不仅可提高精度，同时亦能充分反映超塑变形工艺参数对损伤的影响规律。因此，这就为研究超塑变形时的空洞损伤提供了一种新方法，同时也为神经网络的应用开辟了一个新领域。     

Prediction of Crack Location in Deep Drawing Processes Using Finite Element Simulation

Sheet metal forming process like deep drawing subjected to large irreversible deformation. It leads to high strain localization zones and then internal or superficial micro defects. The deformation behavior and crack initiation in cylindrical deep drawing of aluminum alloy are simulated by the elasto-plastic finite element simulation. A1100-O and A2024-T4 sheet material are used in the simulation. Material properties based on the tensile and plane strain test is used in the simulation. Six cases are simulated in this study with different blank diameter. The simulated results are compared with the experimental results in terms of the crack location and critical punch displacement. The comparison of simulated results with experimental results shows a good agreement.     

The Effect of Micro Damage on Time-Dependent Crack Growth in a Composite Solid Propellant

The damage characteristics near the crack tip and crack growth behaviorin a centrally cracked sheet specimen of a solid propellant wereinvestigated. The specimen was subjected to a constant crosshead speed of0.508 mm/min at room temperature. The effects of local damage andfracture process near the crack tip on crack growth behavior wereinvestigated and results are discussed.     

Investigation of Progressive Damage and Fracture in Laminated Composites Using the Smeared Crack Approach

The smeared crack approach (SCA) is revisited to describe post-peak softening in laminated composite materials. First, predictions of the SCA are compared against linear elastic fracture mechanics (LEFM) based predictions for the debonding of an adhesively bonded double cantilever beam. A sensitivity analysis is performed to establish the influence of element size and cohesive strength on the load-deflection response. The SCA is further validated by studying the in-plane fracture of a laminated composite in a single edge bend test configuration. In doing so, issues related to mesh size and their effects (or non-effects) are discussed and compared against other predictive computational techniques. Finally, the SCA is specialized to orthotropic materials. The application of the SCA is demonstrated for failure mechanics of the open hole tension test, where fiber/matrix fracture is predominant and predicted well by the present approach.     

From Fracture to Damage Mechanics: A behavior law for microcracked composites using the concept of Crack Opening Mode

Many studies have been carried out in order to build a coherent macroscopic behavior law for a composite containing microcracks. All of them are only partially coherent and none of them is complete. This study proposes a hyperelastic behavior law for a microcracked composite, respecting all the conditions associated with the damage activation/deactivation, stress/strain relation continuity, induced anisotropy and the Clausius–Duhem inequality. This approach is based on the definition of the Crack Opening Mode for Damage Mechanics as it exists in Fracture Mechanics.