Process zone analysis for the single-edge notched specimen: Part II. Process zone growth and crack propagation

Process zone growth and crack propagation in the single-edge notched (SEN) specimen are studied using the relations among applied load, notional crack and process zone lengths, and crack opening displacement derived in the first part of this work [1]. Process zone growth is simulated by increasing the notional crack length while keeping the traction-free crack length constant. A model for crack propagation based on either critical crack tip opening displacement (CTOD) or critical process zone length, as criteria for traction-free crack extension is proposed. The influence of closing pressure distribution, initial traction-free crack length, and crack extension criterion on the behavior of load vs. CMOD curves is discussed. The present model can be used to model load-deformation behavior from initial loading through softening to failure of nonlinear materials, as is verified by comparing the theoretical and experimentally determined load vs. crack mouth opening (CMOD) curves for concrete beams.     

Investigation of fatigue crack closure using multiscale image correlation experiments

Two full-field macroscale methods are introduced for estimating fatigue crack opening levels based on digital image correlation (DIC) displacement measurements near the crack tip. Crack opening levels from these two full-field methods are compared to results from a third (microscale) method that directly measures opening of the crack flanks immediately behind the crack tip using two-point DIC displacement gages. Of the two full-field methods, the first one measures effective stress intensity factors through the displacement field (over a wide region behind and ahead of the crack tip). This method reveals crack opening levels comparable to the limiting values (crack opening levels far from the crack tip) from the third method (microscale). The second full-field method involves a compliance offset measurement based on displacements obtained near the crack tip. This method delivers results comparable to crack tip opening levels from the microscale two-point method. The results of these experiments point to a normalized crack tip opening level of 0.35 for R ∼ 0 loading in grade 2 titanium. This opening level was found at low and intermediate ΔK levels. It is shown that the second full-field macroscale method indicates crack opening levels comparable to surface crack tip opening levels (corresponding to unzipping of the entire crack). This indicates that effective stress intensity factors determined from full-field displacements could be used to predict crack opening levels.     

Multivariate Adaptive Regression Splines Model to Predict Fracture Characteristics of High Strength and Ultra High Strength Concrete Beams

This paper presents Multivariate Adaptive Regression Splines (MARS) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). This paper also presents the details of development of MARS model to predict failure load (Pmax) of high strength concrete (HSC) and ultra high strength concrete (UHSC) beam specimens. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. MARS model has been developed by establishing a relationship between a set of predicators and dependent variables. MARS is based on a divide and conquers strategy partitioning the training data sets into separate regions; each gets its own regression line. Four MARS models have been developed by using MATLAB software for training and prediction of fracture parameters and failure load.MARS has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed from the studies that the predicted values of Pmax, GF, KIC and CTODC are in good agreement with those of the experimental values.     

Strip yield analysis of two collinear unequal cracks in an infinite sheet

Plastic zone sizes and crack tip opening displacements (CTODs) are obtained for two collinear cracks in an infinite sheet subjected to known remote stress. Analysis is conducted by assuming the crack accompanying plastic zones as a fictitious crack and formulating integral equations based upon traction free and no stress singularity conditions. In addition, critical remote stress, plastic zone sizes, and CTODs when the adjacent plastic zones touched are obtained by assuming the coalesced fictitious cracks as a single fictitious crack and formulating integral equations based upon no stress singularity and zero coalesced point displacement conditions. Extensive numerical results are presented.     

聚丙烯纤维水泥稳定碎石断裂性能试验研究

通过30个尺寸为100mm×100mm×515mm的聚丙烯纤维水泥稳定碎石和普通水泥稳定碎石三点弯曲试件断裂试验,探讨了聚丙烯纤维对水泥稳定碎石断裂韧度(KIC)、断裂能(GF)、临界裂缝嘴张开位移(CMODC)、临界裂缝尖端张开位移(CTODC)、极限裂缝嘴张开位移(CMODmax)和极限裂缝尖端张开位移(CTODmax)的影响。试验结果表明:聚丙烯纤维的掺入可增大水泥稳定碎石的断裂韧度、断裂能、临界裂缝嘴张开位移、极限裂缝嘴张开位移、临界裂缝尖端张开位移和极限裂缝尖端张开位移;随着聚丙烯纤维体积掺量的增加,断裂韧度、临界裂缝嘴张开位移和临界裂缝尖端位移的变化无明显规律,但断裂能、极限裂缝嘴张开位移和极限裂缝尖端位移基本上呈线性增加的。     

FATIGUE CRACK TIP MECHANICS OF A POWDER METALLURGY ALUMINUM ALLOY IN VACUUM AND HUMID AIR

Abstract— Fatigue crack tip opening displacements and strains in the material very close to the crack tip have been determined from measured displacements for cracks grown in both vacuum and humid air environments. The environment alters both the relations between crack tip opening displacement and crack tip strain, and the effect of cyclic stress intensity on these factors. Results of dynamic observation of intermittent crack growth are correlated with fractographic evidence. The relationships between crack tip parameters are used in a previously developed mathematical model. The effect of wet air on fatigue crack growth is found to be a reduction in crack tip plasticity.     

On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems

The accurate calculation of the opening and closing stresses is an important issue in fatigue crack closure problems, since the effective driving force for crack growth is dependent on accurate calculation of the opening stresses. Often numerical methods such as finite element analysis are used to model plasticity-induced fatigue crack closure problems. There are many difficulties associated with this modelling work, since the results may depend on a wide range of parameters such as mesh refinement, node release scheme and modelling of the contact between the crack faces etc. Even after a great deal of modelling work some arbitrariness is evident in the technique used for assessing the opening and closing stresses. A number of techniques have been proposed in the literature and the current work will assess and compare these approaches. The node displacement method, the change in stresses at the crack tip, and the weight function technique will each be applied to a finite element model of a plane stress crack for a range of stress levels. In addition, an analytical model for plasticity-induced crack closure under plane stress conditions will be used to discuss the accuracy of these techniques. The investigation shows that all these techniques are equivalent provided that the displacement and stress at the crack tip are assessed accurately. However, it will be shown that use of the tensile tip stress method, proposed by some authors for assessing the closing stress, is erroneous.     

Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs’ parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs’ parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.     

Crack Growth Across a Strength Mismatched Bimaterial Interface

Crack growth across an interface between materials with different strength is examined by a cohesive zone model. The two materials have identical elastic properties but different fracture process properties, or different yield stresses, which is modeled by different cohesive stresses. The fracture criteria is a critical crack opening displacement. Load is represented by a stress intensity factor defining a remote square root singular stress field. The results show that the ratio between the cohesive stresses of the two materials primarily determines the behavior of the critical stress intensity factor. When the crack approaches a material with a higher cohesive stress the crack tip is shielded, but if the crack approaches a material with smaller critical crack opening displacement the maximum level of shielding is determined by the ratio between the critical crack opening displacements. When a crack approaches a material with a lower cohesive stress it is exposed to an amplified load. This revised version was published online in August 2006 with corrections to the Cover Date.     

Weight functions and strip yield solution for two equal-length collinear cracks in an infinite sheet

The problem of two equal-length collinear cracks in an infinite sheet is treated using the weight function method. Exact weight functions for the inner and outer crack tips are derived based on the crack opening displacement solution for a reference load case. These weight functions are used to calculate stress intensity factors for different load cases, plastic zone sizes and crack tip opening displacements of the strip yield model. The approach is validated by the perfect agreement between the present strip yield model solutions and Collins and Cartwright’s analytical results based on the direct complex stress function formulation.     

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50-50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.     

A numerical Green's function and dual reciprocity BEM method to solve elastodynamic crack problems

A computational model based on the numerical Green's function (NGF) and the dual reciprocity boundary element method (DR-BEM) is presented for the study of elastodynamic fracture mechanics problems. The numerical Green's function, corresponding to an embedded crack within the infinite medium, is introduced into a boundary element formulation, as the fundamental solution, to calculate the unknown external boundary displacements and tractions and in post-processing determine the crack opening displacements (COD). The domain inertial integral present in the elastodynamic equation is transformed into a boundary integral one by the use of the dual reciprocity technique. The dynamic stress intensity factors (SIF), computed through crack opening displacement values, are obtained for several numerical examples, indicating a good agreement with existing solutions.     

Cyclic crystal plasticity analyses of stationary, microstructurally small surface cracks in ductile single phase polycrystals

ABSTRACT This paper explores the effects of microstructural heterogeneity on the cyclic crack tip opening and sliding displacements for stationary, microstructurally small transgranular surface cracks in a single phase metallic polycrystal using planar double slip crystal plasticity computations. Crack tip displacements are examined under plane strain conditions for stationary cracks of different lengths relative to grain size as a function of the applied nominal strain amplitude for tension-compression and cyclic shear. Nominal strain amplitudes range from well below to slightly above the nominal cyclic yield strength for each type of loading condition. Results indicate the complex nature of the crack tip sliding and opening displacements as functions of nominal strain amplitude and orientation of the nearest neighbour grains, the influence of the free surface in promoting the cyclic opening displacement even for cracks in the first surface grain, the rather restricted limits of applicability of linear elastic fracture mechanics, and very interesting crack tip plasticity effects which include crack tip displacement ratcheting or progressive accumulation, even for completely reversed, proportional applied loading. Results are compared for cases with and without crack face friction.     

ANN Model to Predict Fracture Characteristics of High Strength and Ultra High Strength Concrete Beams

This paper presents fracture mechanics based Artificial Neural Network (ANN) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (Gf), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). Failure load of the beam (Pmax) is also predicated by using ANN model. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. Back-propagation training technique has been employed for updating the weights of each layer based on the error in the network output. Levenberg- Marquardt algorithm has been used for feed-forward back-propagation. Four ANN models have been developed by using MATLAB software for training and prediction of fracture parameters and failure load. ANN has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed from the studies that the predicted values of Pmax, Gf, failure load, KIc and CTODc are in good agreement with those of the experimental values.     

A novel multiscale approach to brittle fracture of nano/micro‐sized components

Principles and advantages of a new concept based on the ab initio aided strain gradient elasticity theory are shown in comparison with the classical Barenblatt cohesive model. The method is applied to the theoretical prediction of the critical energy release rate and the crack tip opening displacement at the crack instability in nanopanels made of germanium and molybdenum crystals. The necessary length scale parameter l₁ is determined for germanium and molybdenum by the best gradient elasticity fits of ab initio computed screw dislocation displacements and phonon dispersions. Values of ab initio computed critical energy release rates and crack opening profiles revealed that the length l₁ is related to inflexion points of profiles. A novel ab initio method in combination with continuum mechanics was successfully tested to replace molecular statics dependent of availability of interatomic potentials. The asymptotic strain gradient elasticity solution for displacement components near the crack tip in materials with cubic lattice was also derived.     

Measurement of crack closure points during cyclic loading by the strain interference method

Effective stress intensity factor range ΔK_eff and J integral range ΔJ, which are determined using the crack tip opening or closing point, have been considered as the reasonable parameters controlling crack propagation behavior. Therefore, the development of a simple and practical measurement method of crack tip opening and closing stress is considered to be important for the evaluation of crack propagation. In this study, for a center-cracked plate in the elastic-plastic condition, it is shown that the crack tip opening and closing points can be easily determined with the relationship between the nominal cyclic stresses and the local strains measured in the vicinity of the crack center. Then, this measurement method is compared with the results obtained by the finite element method calculation.     

THE EFFECT OF WATER VAPOR ON FATIGUE CRACK TIP MECHANICS IN 7075-T651 ALUMINUM ALLOY

Abstract— Strains very near a growing fatigue crack have been computed from measured material displacements, both for a very dry environment and for humid air. Significant differences in crack tip strains arid crack tip opening displacements occur in these environments, with crack tip deformation in water vapor evidencing less plasticity than the dry environment. These quantitative results are incorporated into a previously developed mathematical model which is based, in part, on dynamic observations of intermittent crack growth. Fractography is shown to support the concepts of intermittent crack advance and decreased crack tip plasticity due to environmental water vapor.     

Elastic-plastic analysis of stress state and spread of plastic zone around single edge-cracked plate by finite element method

A two-dimensional finite element model for estimating elastic-plastic displacements and stresses near a crack for the elastic-plastic situation of loadings is presented. Singularity effects near the crack tip are solved by introducing 12-node cubic isoparametric elements in the crack tip region and collapsing them into triangular elements. The proposed finite element model is used to determine the spread of the plastic zone and mouth opening displacements of an edge-cracked structural steel plate. The spread of the plastic zone is obtained by successive increments of applied nominal tensile stress transverse to the crack length. The mouth opening displacement values obtained by this model are also compared with those measured experimentally.     

On the fracture behavior of a Zener–Stroh crack with plastic zone correction in three-phase cylindrical composite material

With crack tip plastic zone correction, stress investigation on the fracture behavior of a Zener–Stroh crack in three-phase composite was carried out. A Zener–Stroh crack (in the matrix phase) is near a circular inclusion, with the three-phase cylindrical composite model used to represent the composite material. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. The Dugdale model of small scale yielding is used to introduce a thin strip of yielded plastic zone each crack tip. The physical problem is formulated into a set of singular integral equations, using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function. The singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements using Erdogan and Gupta’s method with some iterative numerical procedures.     

Simplified equations for determining double‐K fracture parameters of concrete for 3‐point bending test

The paper presents simplified polynomial equations for determining the double‐K fracture parameters of concrete for 3‐point bending beams with variable strengths and material properties of concrete. The derived equations avoid complexities involved in computations of fracture parameters using existing analytical methods. The input data required for systematic computation in the study for deriving the nondimensional fracture parameters are obtained using a fictitious crack model. It is inferred that for a relative size of initial crack length, critical load and corresponding crack opening displacement maintain a linear relationship in their nondimensional forms. The value of critical mouth opening displacement can also be determined for known value of peak load using the derived nondimensional equation, thus avoiding the measurement of the crack mouth opening displacement in the experiment. Further, the derived polynomial equations predict the double‐K fracture parameters of concrete with negligible error as compared to those obtained based on experimental results.