A Strip-Yield algorithm for the analysis of closure evaluation near the crack tip

“Plasticity-induced crack closure” phenomenon is the leading mechanism of different effects (R-ratio, overload retardation, … ) acting on crack growth rate in many metallic materials. Experimental tests are carried out to quantify the physical phenomenon, while Strip-Yield analytical models have been developed for predicting life of components. In the present work, an additional module to be applied to a Strip-Yield model is proposed in order to derive the strains near the crack tip. Particularly, the module is based on the Westergaard’s elastic complex potential. The presented algorithm allowed us to obtain the correlation between “local compliance” experimental results and the corresponding Strip-Yield analyses. This method can be taken as a semi-analytical procedure for calibrating the constraint factor, i.e., the most delicate parameter for Strip-Yield models.     

Variable amplitude fatigue crack growth in a mild steel for railway axles: Experiments and predictive models

Railway axles, though designed for infinite life, are subject to failure due to various types of surface damage (ballast hits, corrosion) that might occur during their very long service life (30 years or 10⁷ km). This problem is dealt with by regular axle examinations in the form of nondestructive testing inspections, whose periodicity is calculated on the basis of the propagation lifetime of a given initial defect. The key point is therefore a reliable estimation of propagation lifetime under service loads.This paper discusses the application of predictive crack growth algorithms to the propagations of cracks in A1N steel axles. In particular, constant amplitude crack propagation tests on small-scale and “companion specimens” were carried out together with experiments on full-scale axles. Variable amplitude tests on companion specimens were performed and the results were then analysed using a simple “no-interaction” algorithm. Then, variable amplitude tests on companion specimens and the analysis of results with a simple “no-interaction” algorithm and the Strip-Yield model were dealt with.The results showed a negligible load-interaction effect on “companion specimens” and a significant retardation on full-scale axles. The consequences resulting from the application of predictive models to a full-scale axle under service spectrum were then analysed.     

Load interaction effects in propagation lifetime and inspections of railway axles

As well known, an interaction effect arises, on crack propagation, when a specimen or a component is subjected to variable amplitude fatigue loading. Depending on the applied load sequence, a certain amount of retardation or acceleration can then be observed, on the fatigue crack growth rate, with respect to the constant amplitude case. In the case of structural ductile materials, the interaction phenomenon is mainly addressed by the local plasticity at the crack tip and can be explained, from a global point of view, by adopting the crack closure concept. In the present research, load interaction effects in a medium strength steel for railway axles are experimentally analyzed by companion and full-scale specimens. The experimental outcomes show a significant retardation with respect to a simple no-interaction approach and the Strip-Yield model offers good, yet conservative, estimates of crack advance. The consequences of crack growth retardation on the inspection periodicity of railway axles are then discussed.     

T-stress and its implications for crack growth

Some of the “irregular” crack growth behaviour observed in different specimen geometries may not be unrelated. Discrepancies in fatigue crack growth rate have been observed in different specimen geometries of the same material; crack front “tunnelling” and out-of-plane crack growth have been found in mode I tension at elevated temperature. The results presented in this paper seem to indicate the relevance of a crack tip constraint parameter, the elastic T-stress, to the irregular crack growth behaviour that conventional LEFM fails to explain.     

Derivation of effective stress intensity factors from measured crack face displacements

When a crack is subjected to cyclic shear-mode loading, crack faces interference wedge the crack open and reduce the effective ΔK_II. The methods proposed in the literature to prevent it or to derive the effective ΔK_I and ΔK_II are discussed. It is shown that when crack tip plasticity becomes important it tends to make displacements larger than those predicted by LEFM and to “hide” friction effects. Finite element simulations combining friction and plasticity can separate these two effects, but the analysis of force-sliding displacement loops derived from displacement field measurements based on image correlation is a more straightforward and efficient method.     

Compliance calibration of the short rod chevron-notch specimen for fracture toughness testing of brittle materials

The short rod chevron-notch specimen has the advantages of (1) crack development at the chevron tip during the early stage of test loading and (2) convenient calculation of K _Ic from the maximum test load and a calibration factor which depends only on the specimen geometry and manner of loading. For generalized application, calibration of the specimen over a range of specimen proportions and chevron-notch configurations is necessary. Such was the objective of this investigation, wherein calibration of the short rod specimen was made by means of experimental compliance measurements converted into dimensionless stress intensity factor coefficients.     

Damage evolution and characterisation of crack types in CF/EP laminates loaded at low temperatures

Tensile testing of CF/EP AS4/8552 cross-ply laminates at room (RT) and cryogenic (around −150 °C) temperatures has been performed to study the effect of temperature on damage (intralaminar cracking) evolution. Microscopy studies of the specimen edges showed a significant difference in damage pattern for the two different temperatures. At the low temperature (LT), more complex crack types were obtained that could not be found in specimens tested at the RT. The effect of these crack types on the laminate tensile modulus was studied by FEM. In analytical stiffness modelling complex shape crack was replaced by an “effective” normal (straight) crack with an “effective” crack opening displacement (COD) that leads to the same reduction in laminate stiffness. A crack efficiency factor was introduced to characterize the significance of complex crack shapes for stiffness reduction. The reduction of tensile modulus for a laminate damaged at low temperature was measured and compared with model predictions.     

The effect of crack tunneling on crack growth: experiments and CTOA analyses

This paper compares experimental crack-front shapes recorded at various stages of crack growth with area-average crack growth values during fracture tests conducted on 2024-T351 aluminum alloy plate. Crack-front shapes were determined by fracturing the specimen to a predetermined amount of crack growth and fatigue cycling the specimen for about 4000 cycles at a high stress ratio (P_min/P_max) to mark the crack-front location. For each shape, the area-average crack length was determined. The evolution of tunneling was used to create a calibration curve that could be used to adjust surface measured crack-length values, for a more representative comparison with analyses that use a straight crack-front approximation. The analysis compares much more favorably with the average crack growth than with the surface measured values near maximum load. However, the area-average technique tends to over correct crack growth near the crack initiation load. Crack tunneling results show that the area-average technique produces more representative crack-length measurements compared to optical based surface measurements.     

Measurement of crack propagation data in small slices of brittle materials in controlled bending

Measuring slow crack propagation data in small slices of brittle materials, elongations were cemented to both sides giving a four-point bend specimen. A method of introducing a definite sharp crack was employed to enable displacement-controlled fracture experiments to be performed. For the evaluation of the load-displacement plots of controlled fracture experiments an experimental compliance calibration was done for measuring crack length from compliance. The method to determine the curve of crack resistance against crack velocity was tested with window glass, giving good agreement between measurements on homogeneous and cemented specimens, if internal stresses from preparation are negligible.     

Examination of the 4-ENF test for measuring the mode III R-curve of wood

The four-point bend end-notched flexure (4-ENF) test, which was originally developed for measuring the mode II R-curve, is thought to be applicable for measuring the mode III R-curve. In this study, a 4-ENF fracture test of spruce was conducted for obtaining the mode III R-curve, and the test method was numerically and experimentally analyzed. In the numerical analysis, three-dimensional finite element calculations were conducted to determine the distribution of the strain energy release rate along the delamination front by the virtual crack closure technique (VCCT). In the experimental analysis, the mode III R-curve was examined by the modified beam theory and compliance calibration methods of data reduction, which have been conventionally used for analyzing the mode I or mode II R-curve. In addition to these conventional data reduction methods, the strain at each loading point was measured, as was the loading-line displacement and critical load for crack propagation, and the R-curve was obtained by the combination of loading-line compliance, load-longitudinal strain compliance, and critical load for crack propagation, which is named the “compliance combination method”. The finite element analyses suggested that the pure mode III fracture state existed in the mid-section of the specimen in spite of the existence of a small mode II component at the free edges of the delamination front, and the mode III strain energy release rate component calculated by the VCCT coincided well with those obtained by the data reduction methods examined here. The actual R-curve obtained by the compliance combination method coincided well with those by the modified beam theory and compliance calibration methods when the strain was appropriately measured. From these results, therefore, the 4-ENF fracture test is a promising means for obtaining the mode III R-curve of wood.     

Tapered beam on elastic foundation model for compliance rate change of TDCB specimen

A modified beam theory is developed to predict compliance rate change of tapered double cantilever beam (TDCB) specimens for mode-I fracture of hybrid interface bonds, such as polymer composites bonded to wood. The analytical model treats the uncracked region of the specimen as a tapered beam on generalized elastic foundation (TBEF), and the effect of crack tip deformation is incorporated in the formulation. A closed-form solution is obtained to compute the compliance and compliance vs. crack length rate change. The present TBEF model is verified with finite element analyses and experimental calibration data of compliance for wood-wood and wood-composite bonded interfaces. The compliance rate change can be used with experimental critical fracture loads to determine the respective critical strain energy release rates or fracture toughness of interface bonds. The present analytical model, which accounts for the crack tip deformation, can be efficiently and accurately used for compliance and compliance rate-change predictions of TDCB specimens and reduce the experimental calibration effort that is often necessary in fracture studies. Moreover, the constant compliance rate change obtained for linear-slope TDCB specimens can be applied with confidence in mode-I fracture tests of hybrid material interface bonds.     

Evolution of residual stresses with fatigue loading and subsequent crack growth in a welded aluminium alloy middle tension specimen

Neutron diffraction has been used to measure the evolution of the residual stresses in a VPPA welded Al-2024 alloy middle tension (M(T)) specimen with fatigue loading and subsequent crack growth. The measurements were carried out on the diffractometer ENGIN-X, a time-of-flight instrument, at the ISIS Pulsed Neutron Source. Fatigue crack growth was performed in situ and strain measurements averaged through the thickness of the specimen were made along two orthogonal directions as the crack grew, allowing the stresses in the specimen to be calculated assuming plane stress. 2D finite element simulation of the evolution of the initial residual stress field with crack growth, using an elastic model produced predictions that were in reasonable agreement with the experimental results. The results further indicate that some re-distribution of the residual stress field occurred due to the crack tip plasticity associated with the fatigue loading.     

Numerical simulations of specimen size and mismatch effects in ductile crack growth - Part I: Tearing resistance and crack growth paths

The Gurson-Tvergaard-Needleman (GTN) model has been used for detailed numerical simulations of the effects of specimen size and yield stress mismatch on ductile crack growth behaviour in two different finite specimen geometries. For deep cracked bending specimens the crack growth resistance, expressed through the far-field J, increases as the specimen size is reduced, most strongly seen in case of low hardening. An opposite effect can be seen to some extent for shallow cracked specimens loaded in tension for low and intermediate hardening. For the yield stress mismatch cases low hardening and bend loading are found to promote crack growth deviation away from the initial crack plane.     

Numerical evaluation of the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests

Nonlinear finite element analyses are used to examine the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests. Energy release rates are first determined by a recently developed direct energy balance approach. It is shown that the finite diameter loading rollers that are typically used in practical test set-ups cause both tests to be inherently nonlinear. The effect of these nonlinearities on the energy release rate is shown to be larger in the four point than the three point test and to increase with increasing roller diameter, increasing coefficient of friction along the crack plane, and decreasing supporting span length. For the four point test, the effect of these nonlinearities is also shown to increase with increasing ratio of inner to outer span length. Next, energy release rates at the onset of crack advance are determined by a simulated compliance calibration technique. This “perceived toughness” is compared with predictions of the “true toughness” given by the direct energy balance approach at the same load. It is shown that perceived toughnesses from this simulated compliance calibration procedure are larger than previously reported results that were obtained in a similar fashion using linear theory. In addition, the perceived toughness is shown to strongly depend upon the range used for fitting the load versus deflection data to obtain compliance. These findings are used to make some general recommendations regarding use of the two test methods and their associated data reduction techniques.     

Theoretical and numerical modelling of creep crack growth in a carbon-manganese steel

This paper presents an analytical and numerical study of time dependent crack growth at elevated temperatures. A triaxiality dependent damage model is used to represent the multiaxial creep ductility of the material and an analytical model to predict steady state crack growth in terms of the fracture parameter C^∗, designated the NSW-MOD model, is presented. This model is an enhancement of the earlier NSW model for creep crack growth as it accounts for the dependence of stress and strain on angular position around the crack tip. Elastic-creep and elastic-plastic-creep finite element analyses are performed for a cracked compact tension specimen and the crack propagation rate in the specimen is predicted. It is found that in general the NSW-MOD model gives an accurate estimate of the crack growth rate when compared to the finite element predictions and experimental data for a carbon-manganese steel. However, crack growth rates predicted from the finite element analysis at low values of C^∗ may be higher than those predicted by either the NSW or NSW-MOD model. This enhanced level of crack growth may be associated with the non-steady state conditions experienced at the crack tip.     

Determination of dynamic crack resistance of ductile cast iron using the compliance ratio key curve method

The compliance ratio method is an analytical approach for instantaneous crack length determination in dynamic single-specimen J-R curve testing of ferritic ductile cast iron (DCI). Comparison testing at room temperature and −40 °C was applied to PCVN and SE(B)15 specimens to examine their performance and suitability for the dynamic key curve method for DCI. An experimental reference database of dynamic crack resistance curves was set up by low-blow multiple-specimen tests and used to validate the results of the CR method. The influence of test temperature, microstructure, loading rate and specimen geometry on fracture behavior of the tested DCI was investigated in great detail and these parameters were linked to fracture mechanical properties. The results obtained show that the CR method is suited to establish valid dynamic crack resistance curves for both types of specimen. Nevertheless, SE(B)15 specimens are preferred for dynamic J-R curve determination of DCI based on their advantages such as higher accuracy.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Analytical modelling of dynamic fracture and crack arrest in DCB specimens under fixed displacement conditions

An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded double cantilever beam (DCB) specimen. Fixed displacement condition is prescribed at the pin location under which crack arrest occurs. In the static case, at first, the compliance function of a DCB specimen is obtained and shows good agreement with the experimental results cited in the literature. Afterward, the stress intensity factor is determined at the crack tip via the energy release rate formula. In the dynamic case, the obtained governing equations for the model are solved supposing quasi‐static treatment for unstable crack propagation. Finally, a closed form expression for the crack propagation velocity versus beam parameters and crack growth resistance of the material is found. It is shown that the reacceleration of crack growth appears as the crack tip approaches the finite boundary. Also, the predicted maximum crack propagation velocity is significantly lower than that obtained via the Euler–Bernoulli theory found in the literature.     

Estimation of fatigue crack growth behavior for small-sized C-shaped inside edge-notched tension (CIET) specimen using compliance technique

Being restricted by the relative larger size requirement, traditional and standard fracture specimens are not applicable for the estimation of fatigue crack growth behavior of some very finite-sized components and precious materials. This study develops a small-sized C-shaped inside edge-notched tension (CIET) specimen which has an advantage of specimen minimization and a wide range of adaptability. A systemic compliance technique for estimating fatigue crack growth behavior of CIET specimen has been successfully constructed and experimentally verified. Groups of fatigue crack propagation rate tests of both CIET specimen and CT specimen for 5083-H112 aluminum alloy were carried out. The resulted da/dN ∼ ΔK curves are heavy affected by specimen configuration and load ratio, and the difference between these da/dN ∼ ΔK curves has been successfully removed by introducing the correction of plasticity-induced crack closure effect. Consequently, the feasibility of CIET specimen for estimating fatigue crack propagation behavior for small-sized components and precious materials has been evidently confirmed.     

Design and analysis of the crack rail shear specimen for mode III interlaminar fracture

The crack rail shear (CRS) specimen is a proposed test method to characterize the Mode III interlaminar fracture toughness of continuous-fiber-reinforced composite materials. The specimen utilizes the two-rail shear test fixture, and contains embedded Kapton film placed symmetrically about the midplane to provide starter cracks for subsequent characterization. Otherwise, specimen length and width are identical to the ASTM shear test specimen geometry. An analytical expression for the strain energy release rate is developed based on a strength of materials approach. The model illustrates the important material and geometric parameters of the test, and provides a simple data reduction scheme for experiments. A quasi three-dimensional, linear elastic finite element code, CCMQ3D, is employed to verify the pure Mode III fracture state and to determine admissible crack lengths. Deformation of the model shows that only the out-of-plane displacement is non-zero, indicating that a pure Mode III fracture state does indeed exist within the constraints of the Q3D assumption. Compliance and strain energy release rate predictions are in good agreement with the strength of materials model over the range of crack lengths, 0·15<a/w<0·85. A fully three-dimensional, linear elastic finite element analysis of the CRS is employed to quantify the effect of finite length on the fracture state. Only intermediate crack lengths are investigated. Crack closure techniques are utilized to determine the components of the strain energy release rate present. Results indicate that a small boundary layer of mixed mode behavior exists at the free edges that diminishes to a pure Mode III fracture state. Compliance and strain energy release rate predictions by the 3D model show good agreement with the Q3D and strength of materials models.