A plastic fracture mechanics model for characterization of multiaxial low-cycle fatigue

The near-tip stress and strain fields of small cracks in power-law hardening materials are investigated under plane-stress, general yielding, and mixed mode I and II conditions by finite element analyses. The characteristics of the near-tip strain fields suggest that the experimental observations of shallow surface cracks (Case A cracks) propagating in the maximum shear strain direction can be explained by a fracture mechanics crack growth criterion based on the maximum effective strain of the near-tip fields for small cracks under general yielding conditions. The constant effective stress contours representing the intense straining zones near the tip are also presented. The results of the J integral from finite element analyses are used to correlate to a fatigue crack growth criterion for Case A cracks. Based on the concept of the characterization of fatigue crack growth by the cyclic J integral, the trend of constant J contours on the Γ-plane for Case A cracks compares well with those of constant fatigue life and constant crack growth rate obtained from experiments.     

Energy-based r-adaptivity: a solution strategy and applications to fracture mechanics

This paper deals with energy based r-adaptivity in finite hyperelastostatics. The focus lies on the development of a numerical solution strategy. Although the concept of improving the accuracy of a finite element solution by minimizing the discrete potential energy with respect to the material node point positions is well-known, the numerical implementation of the underlying minimization problem is difficult. In this paper, energy based r-adaptivity is defined as a minimization problem with inequality constraints. The constraints are introduced to restrict the maximum distortion of the finite element mesh. As a solution strategy for the constrained problem, we use a classical barrier method. Beside the theoretical aspects and the implementation, a numerical experiment is presented. We illustrate the performance of the proposed r-adaptivity in the case of a cracked specimen.     

Studies on fracture model and mechanism for compressed cast iron specimen

Based on the results of acoustic emission monitoring and electron microscope observing, the author of the paper proposes a mechanics model for compressed cast iron specimen—a column with internal inclined crack. Then numerical simulations for the model are made and the distributions of SIF K_i (i = I, II, III) along the crack front are obtained and so the fracture mechanism of suen kind of specimen is found. Finally, according to the theory of strain energy density factor, the critical fracture angle is obtained by using the known SIF. When the friction between the crack surfaces is taken into account, the fracture angle calculated agrees well with experimental results of compressed cast iron in a general laboratory.     

Energy-based prediction of low-cycle fatigue life of BS 460B and BS B500B steel bars

This paper develops energy-based models for predicting low-cycle fatigue life of BS 460B and BS B500B steel reinforcing bars. The models are based on energy dissipated in the first cycle, in average cycles and in total energy dissipated to failure for strain ratios R = −1, −0.5, and 0. Upon prediction of the low-cycle fatigue life, the total energy dissipated during the entire fatigue life of steel reinforcing bars can also be predicted based on the predicted fatigue life. The results indicated that the hysteresis plastic strain energy dissipated during fatigue loading is an important and accurate parameter for predicting the fatigue life of steel reinforcing bars and that the predictions based on energy dissipated on average cycles are more accurate than those based on energy dissipated in the first cycle. It is concluded that the strain ratio R has a clear effect on the energy dissipation for both materials where BS B500B dissipated more energy than BS 460B for R = −0.5 and 0 and about the same energy for R = −1 for certain range of fatigue life. Other conclusions and observations were also drawn based on the experimental results.     

Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

Finite element analysis of a laser-processed fracture specimen

Finite element analysis was used to simulate the static failure of a AISI 4140, three-point bend, Charpy specimen. Non-linear finite element models (FEM) were constructed to represent standard Charpy, fatigue-precracked Charpy, and laser-processed Charpy specimens. For the laser-processed Charpy FEM, a strain-based failure criterion was used to simulate crack propagation through the 0.5 mm thick laser-processed zone. For comparison, a 0.5 mm long crack was used in the fatigue-precracked FEM and similarly loaded. Results showed that the numerically calculated load for crack initation through this zone compared favorably to that reported in earlier experiments. Furthermore, after the crack had propagated through the laser-processed zone within the FEM-comparison of plastic strain contours for this model and that for a fatigue-precracked model showed that similar patterns exist around the crack tip. These results indicate that laser-processing and fatigue-precracking should provide a similar basis for fracture toughness measurements.     

Elasto-plastic analysis of a mode II fracture specimen

An elasto-plastic analysis of a compact mode II fracture specimen is performed. Both an approximate approach with rigid plastic material and a more exact elasto-plastic finite element calculation are carried out. From this analysis, an -factor is determined relating the J-integral to the internal energy measured along the specimen crack faces. It is shown through the finite element computation that it is justifiable to define an -factor. With this result, it is now possible to perform tests on aluminium specimens so as to determine J _IIc.     

Simulations of fast fracture in the DCB specimen using Kanninen's model

Kanninen's beam model for the DCB specimen is used to analyze several fast fracture problems. First, the model is studied under two loading conditions to which it has not been applied previously: constant-force (dead) loading and rapid-wedge (constant velocity) loading. The predictions of crack propagation under both of these loading conditions are similar to those obtained by Bilek and Burns. Second, the implications of using different methods of simulating the bluntness of a starter-notch are investigated for conditions typical of Kanninen's analyses and experiments conducted at the Battelle Laboratories. The predictions of crack behavior are in general agreement with Kanninen's results; however, it appears that quantitative predictions are sensitive to the specific manner in which the bluntness is simulated in the analytical model.

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Résumé Le modèle en poutre de Kanninen pour les éprouvettes double Cantilever est utilisé en vue d'analyser plusieurs problèmes de rupture rapide. En premier lieu, le modèle est étudié sous 2 conditions de charge pour lesquelles il n'avait pas été appliqué précédemment: la charge constante (point mort) et le chargement rapide de côté (à vitesse constante). Les prédictions de propagation de fissure sous ces 2 conditions de charge sont similaires à celles obtenues par Bilek et Burns. En deuxième lieu, les implications de l'utilisation de différentes méthodes pour simuler l'arrondissement d'une entaille initiale sont étudiées pour des conditions typiques des analyses de Kanninen et des expériences conduites aux Laboratoires du Battelle. Les prédictions du comportement de la fissure sont en général en accord avec les résultats de Kanninen. Toutefois, il apparait que les prédictions quantitatives sont sensibles à la manière spécifique suivant laquelle l'arrondissement est simulé dans le modèle analytique.

     

Endurance of structural materials in complex low-cycle loading

The results of examination of the relationships governing damage cumulation on complex low-cycle loading are presented. A phenomenological criterion of evaluating the kinetics of damages cumulation in the structure of the material is proposed for this purpose. The components of the deviator of additional stresses is determined on the basis of the mutlisurface theory of plastic yielding with Pisarenko-Lebedev loading surfaces. A method of determining the mean parameters of the model is described. The calculated endurance data are compared with the experimental values for VT14 alloy and 14Kh17N2 steel at T=293°K. Experiments were carried out on tubular specimens in the conditions of piecewise-polygonal trajectories of low-cycle deformation.Translated from Problemy Prochnosti, No. 3, pp 3–9, March, 1991.     

Damage of structural materials under complex low-cycle loading

On the basis of the concepts of the continuum mechanics of damage, we propose an engineering method for the analysis of the kinetics of accumulation of scattered defects in metallic structural materials under conditions of elastoplastic deformation and low-cycle fatigue. It is shown that, in the general case of complex loading for the complex stress state, it is reasonable to use the specific energy of additional stresses (with regard for the arc of plastic strains in a loading cycle) as a parameter of damage for two types of fracture (rupture and shear). __________ Translated from Problemy Prochnosti, No. 6, pp. 25–34, November–December, 2007.     

Analysis of a dynamically loaded three-point-bend ductile fracture specimen

The three-point-bend bar is a common specimen configuration used in experimental fracture studies. It is essentially a two-dimensional configuration in the form of a simply supported beam with an initial edge crack on the cross-section at mid-span. The specimen is loaded to fracture initiation by means of a concentrated transverse force applied at mid-span on the uncracked surface of the beam. In the present case, it is assumed that the material of interest is ductile, and that fracture initiation occurs after substantial plastic deformation, which develops in the uncracked ligament under the applied load. Furthermore, it is assumed that the loading is rapidly applied so that material inertia must be taken into account in relating applied loads to crack tip fields. It is supposed that the crack tip conditions are such that the J-integral may be adopted as a characterizing parameter. The main purpose of the present study is to determine conditions under which the value of J at initiation may be inferred from quantities that are directly measurable in an experiment. To this end, J is determined from computed field quantities by means of a crack tip integral that is suitable for finite element procedures. The value of J is simultaneously computed in terms of measurable quantities by means of an appropriate deep crack formula, and implications for fracture testing of tough materials at relatively high loading rates are discussed. The notion of a transition time, defined as the time beyond which a deep crack formula may be used to compute J in an experiment, is introduced on the basis of simple model studies. Calculations are performed for typical specimen dimensions and material properties representative of a high-strength structural steel in a ductile condition.     

CTOA of a stable crack in a thin aluminum fracture specimen

A crack tip opening angle (CTOA) resistance curve was generated from the moiré interferometry data of thin single edge notched (SEN) and central notched (CN), 2024-T3 aluminum fracture specimens. This CTOA resistance curve, which has a steady state value of 6°, was then used to propagate the cracks in elastic–plastic finite element models of the CN specimen and a CN specimen with a simulated multiple site damage. The CTOA of curved crack growth in a biaxial fracture specimen scattered between 4° and 8° but the resultant crack tip opening displacement, which is the vector sum of the mode-I and the mode-II crack tip sliding displacement, remained a constant 0.18 mm. The CTOA of a rapidly propagating crack in 1.6 mm thick, 7075-T6 SEN specimens increased from 4.5° at a low-crack velocity to a constant 7° at the terminal crack velocity.     

Three-dimensional photoelastic calibration of a chevron-notched short-bar fracture specimen geometry

Stress intensity distributions have been experimentally evaluated from cracked photoelastic models of the rectangular chevron-notched short-bar fracture specimen. Two methods were applied to SIF determination from near-tip isochromatic fringes in slices removed perpendicularly to the flaw profiles. No assumption on flaw shape was required in the analysis. Comparisons with experimental and numerical compliance calibrations from the literature are included. Differences between 3-D Finite Element and the present photoelastic SIF distributions are discussed. The observed flaw shapes are compared to others found in different materials. Flaw evolution is interpreted in terms of local SIF variations.