Showing papers on "Crack closure published in 1998"

Load interaction effects during fatigue crack growth under variable amplitude loading : A literature review. Part I : Empirical trends

Abstract: A summary is given of reported trends in fatigue crack growth observed in variable amplitude fatigue tests on metallic materials, specifically on steels, under both simple and complex load histories. The effects of load variables, specimen geometry, material properties, microstructure and environment are considered. Attention is given to the threshold behaviour and small crack effects. The reviewed data suggest that, depending on a particular combination of load parameters, material, geometry and environment, variable amplitude load sequences of the same type can produce either retardation or acceleration in fatigue crack growth.

An anisotropic model of damage and frictional sliding for brittle materials

Abstract: The paper provides important developments for the model of anisotropic damage by mesocrack growth, accounting for unilateral behaviour relative to crack closure (Dragon and Halm, 1996, Halm and Dragon, 1996). Frictional sliding of closed microcrack systems is introduced here as an additional dissipative mechanism, which is considered to be coupled with the primary dissipative mechanism (damage by microcrack growth). Indeed, accounting for frictional sliding completes the description of moduli recovery in the existing model by adding to the normal moduli recovery effect (normal with respect to the crack plane) the substantial recovery of shear moduli. In parallel to damage modelling, the internal variable related to frictional sliding is a second-order tensor. Even if the unilateral effect and friction incipience are characterized by a discontinuity of effective moduli, it is crucial to ensure continuity of the energy and stress-response. Relevant conditions are proposed to ensure this. As far as frictional sliding is concerned, and unlike most of the models based on the classical Coulomb law, the corresponding criterion is given here in the space of thermodynamic forces representing a form of energy release with respect to the sliding internal variable. It appears that the normality rule in the latter space for sliding evolution is not physically contradictory with the observed phenomenon. The pertinence of the proposed theory, relative to the maximum dissipation hypothesis for both mechanisms, is illustrated by simulating loading paths involving damage and friction effects.

Nonlinear Fracture Mechanics for Engineers

Abstract: Overview Introduction Classification of Fracture Mechanics Regimes History of Developments in Fracture Mechanics Review of Solid Mechanics Stress Strain Elasticity Plasticity Consideration of Creep Component Analysis in the Plastic Regime Fully Plastic/Limit Loads Review of Linear Elastic Fracture Mechanics Basic Concepts Crack Tip Plasticity Compliance Relationships Fracture Toughness and Predictive Fracture in Components Subcritical Crack Growth Limitations of LEFM Analysis of Cracks under Elastic-Plastic Conditions Introduction Rice's J-Integral J-Integral, Crack Tip Stress Fields, and Crack Tip Opening Displacement J-Integral as a Fracture Parameter and Its Limitations Methods of Estimating J-Integral Analytical Solutions J-Integral for Test Specimens J for Growing Cracks Numerically Obtained Solutions Tables of J-Solutions Crack Growth Resistance Curves Fracture Parameters under Elastic-Plastic Loading Experimental Methods for Determining Stable Crack Growth and Fracture Special Considerations for Weldments Instability, Dynamic Fracture, and Crack Arrest Fracture Instability Fracture under Dynamic Conditions Crack Arrest Test Methods for Dynamic Fracture and Crack Arrest Constraint Effects and Microscopic Aspects of Fracture Higher Order Terms of Asymptotic Series Cleavage Fracture Ductile Fracture Ductile-Brittle Transition Fatigue Crack Growth under Large-Scale Plasticity Crack Tip Cyclic Plasticity, Damage, and Crack Closure ?J-Integral Test Methods for Characterizing FCGR under Large Plasticity Conditions Behavior of Small Cracks Analysis of Cracks in Creeping Materials Stress Analysis of Cracks Under Steady-State Creep Analysis of Cracks under Small-Scale and Transition Creep Consideration of Primary Creep Effects of Crack Growth on the Crack Tip Stress Fields Crack Growth in Creep-Brittle Materials Creep Crack Growth Test Methods for Characterizing Creep Crack Growth Microscopic Aspects of Creep Crack Growth Creep Crack Growth in Weldments Creep-Fatigue Crack Growth Early Approaches for Characterizing Creep-Fatigue Crack Growth Behavior Time-Dependent Fracture Mechanics Parameters for Creep-Fatigue Crack Growth Methods of Determining (Ct)avg Experimental Methods for Characterizing Creep Crack Growth Creep-Fatigue Crack Growth Correlations Case Studies Applications of Fracture Mechanics Fracture Mechanics Analysis Methodology Case Studies Appendices Index

Numerical modeling of fracture coalescence in a model rock material

Abstract: The crack pattern, as well as crack initiation, -propagation and -coalescence observed in experiments on gypsum specimens with pre-existing fractures in uniaxial, biaxial, and tensile loading are satisfactorily predicted with the numerical model presented in this paper. This was achieved with a new stress-based crack initiation criterion which is incorporated in FROCK, a Hybridized Indirect Boundary Element method first developed by Chan et al. (1990). The basic formulation of FROCK is described, and the code verified for both open and closed pre-existing fractures either with only friction or with friction and cohesion. The new initiation criterion requires only three material properties: σcrit, the critical strength of the material in tension; τcrit, the critical strength of the material in shear; r0, the size of the plastic zone. The three parameters can be determined with the results from only one test. Predictions using this model are compared with experiments on gypsum specimens with pre-existing fractures loaded in uniaxial and biaxial compression performed by the authors. Specifically, wing crack and shear crack initiation, crack propagation, coalescence stress and -type as well as the crack pattern up to coalescence can be modeled. The model can also duplicate experimental results in compression and tension obtained by other researchers. These results show that stress-based criteria can be effectively used in modeling crack initiation and crack coalescence.

Experimental Determination of Dynamic Crack Initiation and Propagation Fracture Toughness in Thin Aluminum Sheets

Abstract: An experimental investigation was undertaken to characterize the dynamic fracture characteristics of 2024-T3 aluminum thin sheets ranging in thickness from 1.63–2.54 mm. Specifically, the critical dynamic stress intensity factor Kdc was determined over a wide range of loading rates ( expressed as the time rate of change of the stress intensity factor KdI ) using both a servo- hydraulic loading frame and a split Hopkinson bar in tension. In addition, the dynamic crack propagation toughness, KD, was measured as a function of crack tip speed using high sensitivity strain gages. A dramatic increase in both Kdc and KD was observed with increasing loading rate and crack tip speed, respectively. These relations were found to be independent of specimen thickness over the range of 1.5 to 2.5 mm.

Crack Extension Resistance and Fracture Properties of Quasi-Brittle Softening Materials like Concrete Based on the Complete Process of Fracture

Abstract: The crack extension resistance and fracture properties are studied in detail for quasi-brittle materials like concrete with a softening traction-separation law by investigating the complete fracture process. The computed samples are the three-point bending notched beams of concrete with different sizes tested by other researchers. The softening traction-separation law which was proposed by Reinhardt et al. based on direct tension tests for normal concrete materials was chosen in the computations. Different distribution shapes of the cohesive force on the fictitious crack zone were considered for the corresponding loading states. The computations were mainly based on the analytic solutions for this problem using Gauss–Chebyshev quadrature to achieve the integration which is singular at the integral boundary. The crack extension resistance curves in terms of stress intensity (KR-curves) were determined by combining the crack initiation toughness $$K_{ Ic}^{ini} $$ that is the inherent toughness of the material needed to resist the crack initiation in the case that is in the lack of an extension of the main crack with the contribution due to the cohesive force along the fictitious crack zone during the complete processes of fracture. The situation of crack propagation can be judged by comparing KR-curves of crack extension resistance with the stress intensity factor curves which were calculated using the lengths of the extending crack and the corresponding loads at each loading states, e.g., when the crack extension resistance curve(KR-curve) is lower than the stress intensity factor curve, the crack propagation is stable; otherwise, it is unstable. In the computation, the obtained relationship between the crack tip opening displacement CTOD and the amount of crack extension for the complete fracture process is in agreement with the testing results of other researchers.

Dynamic fracture of a functionally gradient material having discrete property variation

Abstract: A functionally gradient material (FGM) with discrete property variation is prepared, and the dynamic fracture in this material is studied using the technique of photoelasticity combined with high-speed photography Transparent sheets required for the study are made by casting a polyester resin mixed with varying amounts of plasticizer The mechanical (quasi-static and dynamic) and optical properties of the material are evaluated as a function of the plasticizer content Results of material characterization show that the fracture toughness increases with increasing plasticizer content, whereas the Young's modulus decreases The material fringe constant and the dynamic modulus are observed to be relatively insensitive to plasticizer content The FGM is then prepared by casting together thin strips having different plasticizer content The dynamic crack propagation phenomenon is studied for four different property variations along the crack propagation direction, and the effects of these property variations on crack speed, crack jump distance and dynamic stress intensity factor are investigated Results of this investigation show that increasing the toughness in the direction of crack growth reduces the crack jump distance as compared to on increasing-decreasing toughness variation for the same initial energy

Quantification of constraint effects in elastic-plastic crack front fields

Abstract: In-plane and out-of-plane constraint effects on crack tip stress fields under both small-scale and large-scale yielding conditions are studied by means of three-dimensional numerical analyses of boundary layer models and of finite size specimens, M(T) and SE(B), respectively. It is shown that the ratio of the plastic zone size over the panel thickness, rpt, plays a key role in formation of the crack-tip fields, particularly the outof-plane stress components. For a vanishingly small plastic zone around the crack tip the stress fields are dominated by the plane strain solution. With increase of the applied loads, i.e. increasing the plastic zone size, the stress fields develop towards the plane stress state. Characterization of “constraint effects” in terms of Q-stress is investigated. The “second term” in the near tip stress field, which is defined as the difference between the full three-dimensional stress fields and the plane strain reference solution, appears to depend on the distance to the tip and to the free surface of the specimen. Hence, the whole three-dimensional crack front fields cannot be correctly described by a two-parameter formulation as the load increases. However, a unique linear relationship between Q and the hydrostatic stress was found in all three-dimensional crack front fields.

Fatigue crack growth in ferroelectrics driven by cyclic electric loading

Abstract: Fatigue crack growth has been observed recently in ferroelectrics under cyclic electric loading. Does the crack grow by electric breakdown, or by the stress field near the crack tip? The present paper provides a mechanistic explanation for the electric-field-induced fatigue crack growth. The non-uniform electric field near an insulated crack tip might cause domain switching which in turn produces a concentrated stress field characterized by a stress intensity factor. For ferroelectrics poled along a direction perpendicular to the crack, we are able to show quantitatively that: (1) the stress intensity factor under a negative electric field is nine times as large as the stress intensity factor under a positive electric field; (2) the crack starts to grow if the stress intensity factor is higher than the fracture toughness of the material, but the stress intensity factor decreases as the crack extends and eventually results in crack arrest; (3) by reversing the electric field, the stress intensity factor is increased and crack growth resumes; and (4) this model can predict the extent of fatigue crack growth. In contrast to the conventional perception of (mechanical) fatigue, the fatigue crack growth in ferroelectrics under cyclic electric loading is a step by step cleavage process caused by a domain switching sequence that generates a cyclic driving stress field near the crack tip.

Laser shock processing of 2024-T62 aluminum alloy

Abstract: Laser shock processing (LSP) is a relatively new technique for strengthening metals. A method developed for optimizing the LSP parameters is reported in this paper. The effects of LSP on the microstructure, hardness, surface roughness, residual stress, fatigue life, fatigue crack growth (FCG) of 2024-T62 aluminum alloy were investigated. The fatigue life of the laser-shocked specimens was two times greater than that of the unshocked specimens. The fatigue crack growth rates (FCGRs) at a given stress intensity were reduced by over one order of magnitude. The fatigue behavior improvements were attributed to a combination of increased dislocation density, decreased surface roughness and compressive residual stress induced by the laser shock waves.

Nonlinear stress-strain curves for solids containing closed cracks with friction

Abstract: Solutions for the uniaxial stress-strain response of a body containing a distribution of non-interacting nonlinear cracks are derived. First, building on energy formalisms outlined by previous workers, general solutions are derived for the body containing cracks with dissipative tractions at their surfaces, in either tension or compression loading. The special case of a body in compression loading with sliding closed cracks governed by a general friction law is then considered as a case study. The friction law contains two shear resistance terms: a “friction coefficient” term proportional to the resolved normal compression stress across the crack plane; and a “cohesion” term representing the intrinsic shear resistance of the closed crack. Inclusion of the latter term is critical to the existence of a well-defined yield point in the stress-strain curve. It is assumed that the cracks do not extend at their ends during the loading-unloading-reloading cycle; they are, however, allowed to undergo reverse sliding during the unloading. Two crack distributions are considered: all cracks aligned, leading to linear expressions for both the elastic and quasi-plastic stressstrain regions; and cracks randomly oriented, with more complex (but nonetheless tractable) expressions for the quasi-plastic regions. The resultant nonlinear stress-strain curves exhibit cyclic hysteresis, to an extent dependent on friction and crack configuration parameters. Illustrative stress-strain curves are generated for selected ranges of these controlling parameters. An outcome of the analysis is the potential link to microstructural variables, via the crack configuration parameter, offering the prospect for predictions of damage accumulation in real microstructures. The model also offers the prospect of accounting for fatigue properties, via attrition of the frictional resistance at the sliding crack surfaces.

The mode III full-field solution in elastic materials with strain gradient effects

Abstract: The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical KIII field; stresses have r -3/2 singularity near the crack tip, and are significantly larger than the classical K III field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical K III field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical K III field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5 l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral.

Growth of an initially sharp crack by grain boundary cavitation

Abstract: A new computational model is presented to analyze intergranular creep crack growth in a polycrystalline aggregate in a discrete manner and based directly on the underlying physical micromechanisms. A crack tip process zone is introduced in which grains and their grain boundaries are represented discretely, while the surrounding undamaged material is described as a continuum. Special-purpose finite elements are used to represent individual grains and grain boundary facets. The constitutive description of the grain boundary elements accounts for the relevant physical fracture mechanisms, i.e. viscous grain boundary sliding, the nucleation of grain boundary cavities, their growth by grain boundary diffusion and local creep, until coalescence of cavities leads to microcracks. Discrete propagation of the main crack occurs by linking up of neighbouring facet microcracks. Assuming small-scale damage conditions, the model is used to simulate the initial stages of growth of an initially sharp crack under C∗ controlled, mode I loading conditions. Material parameters are varied so as to lead to either ductile or brittle fracture, thus elucidating creep constrained cavitation near cracks. The role of the stress state dependence of cavity nucleation on the crack growth direction is emphasized.

Microscopic fracture processes in a granite

Abstract: The deformation of a competent, brittle, granitic rock is thought to have two main components: elastic and brittle deformation, the latter caused by axial microcracking. Dynamic fatigue testing of Lac du Bonnet granite would, however, suggest the presence of a third mechanism, compaction. Compaction is not the same as elastic crack closure; compaction entails permanent damage along grain boundaries that are under high compression. During compaction, the axial stiffness (elastic modulus) of the rock increases and the permanent crack volume becomes negative (compression). Compaction is active at all stress levels, but it is most noticeable at low stress where its presence is not masked by dilation caused by axial microcracking.

Torsional fatigue of a medium carbon steel containing an initial small surface crack introduced by tension–compression fatigue: crack branching, non‐propagation and fatigue limit

Abstract: In order to examine the threshold condition for the fatigue limit of materials containing a small crack under cyclic torsion, reversed torsional fatigue tests were carried out on 0.47% C steel specimens containing an initial small crack. Initial small semi-elliptical cracks ranging from 200 to 1000 μm in length were introduced by the preliminary tension-compression fatigue tests using specimens containing holes of 40 μm diameter. The threshold condition for the fatigue limit of the specimens containing artificial small defects under rotating bending and cyclic torsion are also reviewed. Crack growth behaviour from an initial crack was investigated. The torsional fatigue limit for a semi-elliptical small crack is determined by the threshold condition for non-propagation of Mode I branched cracks. The torsional fatigue limit of specimens containing an initial small crack can be successfully predicted by the extended application of the √area parameter model in combination with the σ θmax criterion.