Load-point Displacement Curve Research Articles

J-integral testing on micro-scale cantilever beam specimens

The current paper presents a modified procedure for the J-integral testing on micro-scale cantilever beam specimens. For such tests, a non-dimensional factor is required that relates the plastic part of the area below the load vs. load-point displacement curve to J. This parameter is called the “plastic eta-factor”, ηpl. Up to now, a constant value of ηpl≈2 has been used, which is also valid for deeply notched single-edge bend specimens. A comprehensive numerical case study is performed to determine ηpl for cantilever beam specimens as a function of the relative crack length a/W, the relative cantilever length L/W, the relative base distance d/W, and the load, i.e. the degree of plasticity in the specimen. It is shown that ηpl≈2 is applicable only, if the crack length is large, a/W⩾0.5. For smaller a/W-ratios, which are commonly used in the fracture mechanics testing of nano- and micrometer sized materials, ηpl can become much smaller and also dependent on the d/W-ratio. A fitting procedure is presented that enables the determination of the correct value of ηpl, and modifications of the J-integral testing procedure for cantilever beam specimens are proposed. Finally, a numerical validation of the procedure is presented.

An improved fixture for better measuring the displacements and mode‐I fracture toughness of chevron bend specimens

The load versus load point displacement (LPD) curve is significant for the nonlinearity corrections for the mode-I fracture toughness of chevron bend (CB) specimens. The testing fixture plays a crucial role in measuring load versus LPD curves. To better measure the LPDs of CB specimens, we developed an improved fixture system consisting of an understructure and a yoke based on the traditional saddle arrangement fixture suggested by ISRM. With the aid of the improved fixture, continuous synchronized LPDs and CMODs are measured, and nonlinearity corrections are conducted. After nonlinearity corrections, the data of mode-I fracture toughness become more comparable and present a better regularity among different specimen diameters and variant rock types. Repeated tests verify that the improved fixture has the advantages of higher stability and more convenient installation, removal, and adjustment, which can enhance the testing robustness and efficiency.

A comparative study of cohesive zone models for predicting delamination fracture behaviors of arterial wall

AbstractArterial tissue delamination, manifested as the fracture failure between arterial layers, is an important process of the atherosclerotic plaque rupture, leading to potential life-threatening clinical consequences. Numerous models have been used to characterize the arterial tissue delamination fracture failure. However, only a few have investigated the effect of cohesive zone model (CZM) shapes on predicting the delamination behavior of the arterial wall. In this study, four types of CZMs (triangular, trapezoidal, linear–exponential, and exponential–linear) were investigated to compare their prediction of the arterial wall fracture failure. The Holzapfel–Gasser–Ogden (HGO) model was adopted for modeling the mechanical behavior of the aortic bulk material. The CZMs optimized during the comparison of the aortic media delamination simulations were also used to perform the comparative study of the mouse plaque delamination and human fibrous cap delamination. The results show that: (1) the numerical predicted the relationships of force–displacement in the delamination behaviors based on the triangular, trapezoidal, linear–exponential, and exponential–linear CZMs match well with the experimental measurements. (2) The traction–separation relationship results simulated by the four types of CZMs could react well as the corresponding CZM shapes. (3) The predicted load–load point displacement curves using the triangular and exponential–linear CZMs are in good agreement with the experimental data, relative to the other two shapes of CZMs. All these provide a new method combined with the factor of shape in the cohesive models to simulate the crack propagation behaviors and can capture the arterial tissue failure response well.

Experimental and numerical studies of two arterial wall delamination modes.

Arterial wall dissection, which results from various pathophysiological processes, can lead to the occurrence of large area delamination in the aortic wall that can potentially block blood flow and lead to deleterious clinical conditions. Despite its critical clinical relevance, few studies have focused on investigating the failure mode of delamination in the arterial wall. In this study, we quantify the energy release rate of the medial layer of a porcine abdominal aorta via two delamination experiments: the mixed-mode delamination experiment and the "T"-shaped delamination experiment. A cohesive zone model (CZM) is applied to simulate the arterial wall delamination and Holzapfel-Gasser-Ogden (HGO) material model is used to capture the bulk arterial material behavior. A set of parameter values for the HGO and CZM models are identified through matching simulation predictions of the load vs. load-point displacement curve with experimental measurements. Then the parameter values and critical energy release rates obtained from experiments are used as input data for simulation predictions for two arterial wall delamination experiments. The simulation predictions show that the delamination front matches well with experimental measurements. Moreover, the mixed-mode delamination experiment reveals a shear mode-dominated failure event, whereas the "T"-shaped delamination experiment is an opening failure process. The integration of experimental data and numerical predictions of arterial delamination events provides a comprehensive description of distinct failure modes and aids in the prediction of aortic dissection.

A string-based cohesive zone model for interlaminar delamination

The objective of this paper is to develop a string-based cohesive zone model (CZM) for interlaminar delamination, whose associated cohesive elements behave reliably and consistently when deformed along complex separation paths and can display experimental critical energy release rate–mode mixture ratio relationships. Each cohesive element is idealized as a deformable string exhibiting path dependent damage behavior, and the thermodynamic equations are formulated in a generalized standard manner. A damage model having a path dependence function is developed. The rate form of the cohesive law is subsequently derived. The path dependence function is constructed such that each cohesive element can exhibit designated, possibly sophisticated mixed-mode behavior. The interface parameters associated with the present CZM are calibrated from experimental data. The present CZM is validated through simulating a series of flexural tests using Abaqus/Explicit. It is found to be capable of producing reliable simulation results. The interfacial strength is found to affect the predicted applied load–load point displacement curves. The present CZM may be amended to handle other types of fracture or interfacial debonding.

Numerical modeling of experimental human fibrous cap delamination

Fibrous cap delamination is a critical process during the rupture of atherosclerotic plaque, which often leads to severe life-threatening clinical consequences such as myocardial infarction or stroke. In this study a finite element modeling and simulation approach is presented that enables the study of fibrous cap delamination experiments for the purpose of understanding the fibrous cap delamination process. A cohesive zone model (CZM) approach is applied to simulate delamination of the fibrous cap from the underlying plaque tissue. A viscoelastic anisotropic (VA) model for the bulk arterial material behavior is extended from existing studies so that the hysteresis phenomenon observed in the fibrous cap delamination experiments can be captured. A finite element model is developed for the fibrous cap delamination experiments, in which arterial layers (including the fibrous cap and the underlying plaque tissue) are represented by solid elements based on the VA model and the fibrous cap-underlying plaque tissue interface is characterized by interfacial CZM elements. In the CZM, the delamination process is governed by an exponential traction-separation law which utilizes critical energy release rates obtained directly from the fibrous cap delamination experiments. A set of VA model parameter values and CZM parameter values is determined based on values suggested in the literature and through matching simulation predictions of the load vs. load-point displacement curve with one set of experimental measurements. Using this set of parameter values, simulation predictions for other sets of experimental measurements are obtained and good agreement between simulation predictions and experimental measurements is observed. Results of this study demonstrate the applicability of the viscoelastic anisotropic model and the CZM approach for the simulation of diseased arterial tissue failure processes.

Modeling of Experimental Atherosclerotic Plaque Delamination.

A cohesive zone model (CZM) approach is applied to simulate atherosclerotic plaque delamination experiments in mouse abdominal aorta specimens. A three-dimensional finite element model is developed for the experiments. The aortic wall is treated as a fiber-reinforced, highly deformable, incompressible material, and the Holzapfel-Gasser-Ogden (HGO) model is adopted for the aortic bulk material behavior. Cohesive elements are placed along the plaque-media interface along which delamination occurs. The 3D specimen geometry is created based on images from the experiments and certain simplifying approximations. A set of HGO and CZM parameter values is determined based on values suggested in the literature and through matching simulation predictions of the load vs. load-point displacement curve with experimental measurements for one loading-delamination-unloading cycle. Using this set of parameter values, simulation predictions for four other loading-delamination-unloading cycles are obtained, which show good agreement with experimental measurements. The findings of the current study demonstrate the applicability of the CZM approach in arterial tissue failure simulations.

On problems with the determination of the fracture resistance for materials with spatial variations of the Young’s modulus

The paper considers the near-tip J-integral \(\text {J}_{\mathrm{tip}}\), the far-field J-integral \(\text {J}_{\mathrm{far}} \), and the experimental J-integral \(\text {J}^{\mathrm{exp}}\) in a material with sinusoidal variation of the Young’s modulus \(E\). The evaluations of \(\text {J}_{\mathrm{tip}} \) and \(\text {J}_{\mathrm{far}} \) are based on the concept of configurational forces; \(\text {J}^{\mathrm{exp}}\) is evaluated from the area below the load point displacement curve, as prescribed by the standard testing procedures. Analytic expressions and/or approximation formulae are derived, how \(\text {J}_{\mathrm{tip}} ,\,\text {J}_{\mathrm{far}} \) and \(\text {J}^{\mathrm{exp}}\) depend on the system parameters of the material, i.e. wavelength and amplitude of the \(E\)-variation and its phase shift with respect to the crack tip position, and the global specimen dimensions. The analyses show that \(\text {J}_{\mathrm{tip}} \) and \(\text {J}_{\mathrm{far}} \) exhibit a strong dependency on the phase shift, but not the experimental J-integral \(\text {J}^{\mathrm{exp}}\). This is the reason why the current procedures for fracture mechanics testing are not suitable to determine the true values of the fracture initiation toughness \(\text {J}_\mathrm{i} \) or the crack growth resistance \(R\) of a material, if the material properties exhibit a spatial variation in the direction of crack propagation. Relations are given to estimate the possible errors.

The Series <i>K</i> Criterion of Unstable Fracture of Concrete and its Application

The knowledge from extensive investigations showed that the non-linearity of the load and loading point displacement curve is mainly associated with crack propagation. Based on the linear asymptotic superposition assumption, the critical effective crack length is evaluated by analyzing the nonlinear characteristics of the load and loading point displacement curves of a series of the fracture tests. Furthermore, the unstable fracture toughness is determined by inserting the peak load and the critical effective crack length into a formula developed from LEFM. Based on the calculated results, the series K criterion of unstable fracture of concrete fracture is established. At last, an engineering example of cracking analysis of the upstream lock-head foundation of the ship-lift of the Three Gorges Project is given.

Evaluation of Leak-Before-Break (LBB) Behavior For Axially Notched X65 and X80 Line Pipes

Leak-before-break (LBB) behavior was evaluated for two series of API 5L X65 line pipes and three series of X80 line pipes with various levels of Charpy V-notch (CVN) absorbed energy. Full-scale hydrostatic burst tests were conducted for the line pipes with an axial through-wall (TW) notch to determine LBB criteria, that is, the relationship between the axial TW notch length and hoop stress for LBB. The determined LBB criteria were verified by full-scale partial gas burst tests for line pipes with an axial part-through-wall (PTW) notch and were then compared to the estimation using the CVN energy-based equation that Kiefner et al. have proposed. The present study demonstrated that the estimation using the CVN-based equation was in good agreement with the experimental results for the pipes with a relatively low CVN energy of less than 130 J. On the contrary, the equation was not applicable to the pipes with a relatively high CVN energy of more than 130 J. The results of instrumented Charpy tests clarified that the load versus load-point displacement curves for Charpy specimens from the high CVN energy pipes were different from those from the low CVN energy pipes. Therefore, the applicability of the CVN-based equation was dependent on the load versus load-point displacement curve for a Charpy specimen.

Dynamic deformation and fracture behavior of novel damage tolerant discontinuously reinforced aluminum composites

Extrinsically toughened discontinuously reinforced aluminum composites are processed with the objective of enhancing damage tolerance of conventional particle reinforced aluminum composites. The approach consists of producing a composite microstructure in which discrete ductile phases have been incorporated into the particle reinforced metal matrix via traditional powder processing routes. The present study focuses on investigating the effects of volume fraction and flow strength of the ductile phase reinforcements in determining dynamic deformation and fracture characteristics of these extrinsically toughened composites. The dynamic compression behavior of the composites is examined by employing the split Hopkinson pressure bar. The measured dynamic stress–strain response of the composites is correlated with the macro- and micro-damage mechanisms inferred from post examination of the impacted specimens. The dynamic fracture characteristics of the composites are obtained by impact loading pre-cracked three point bend specimens in a modified Hopkinson bar apparatus. The measured load-point force versus load-point displacement curves are used to, (a) estimate the energy required for dynamic crack initiation, and (b) understand the interaction of the dynamically propagating crack tip with the ductile phase reinforcements. The results indicate that the extrinsically toughened DRA composites absorb significantly greater energy during the crack propagation as compared to the conventional DRA composites. Also, the level of extrinsic toughening introduced in the composites is affected by the location, volume fraction and mechanical properties of the ductile phase reinforcements. Amongst the relatively larger volume fraction ductile-phase reinforced composites, the ductile phase reinforcements comprising low flow strength commercial purity aluminum fail primarily in a ductile manner, whereas the ductile phase reinforcements comprising high strength Al alloy fail in a cleavage manner by inter-granular fracture.

Fracture of geometrically scaled, notched three-point-bend bars of high strength steel

The purpose of the experimental work reported in this paper was to provide data that may serve for the development of scaling rules for ductile fracture initiation at blunt notches. Fracture experiments were performed with three sizes of geometrically scaled notched bend specimens of high strength low hardening HY-130 steel using carefully scaled fixturing. Fracture initiation, defined as the appearance of the first sub-millimeter crack with a tensile opening, was reliably detected, using acoustic emission and direct visual inspection with a microscope. Comparison of the normalized load versus load-point displacement curves revealed a significant scale effect on the condition for fracture initiation, with large specimens fracturing at smaller normalized displacement than smaller specimens. The normalized displacement at fracture does not decrease in direct proportion to specimen size. Metallographic cross-sections of the specimens and fractographic observations revealed that at the microscale, fracture initiates by shear localization followed by nucleation and growth of voids under shear and tension in the localization zone. This mechanism profoundly modifies the stress and strain gradients at the notch root so that microstructural length scales become fracture controlling parameters. Both changes are probably responsible for the observed scaling behavior.

Engineering ductile fracture in brittle-matrix composites

This letter describes a newly discovered phenomenon: ductile fracture in cementitious materials. The brittle nature of materials such as concrete and ceramics has prompted the development of various approaches to enhance their fracture toughness. Fibre reinforcement has been the common focus in the toughening of the brittle materials. Two types of fracture have been observed to date in cementitious materials and ceramics: brittle and quasi-brittle fracture. Brittle fracture can be observed, for example, in hardened cement paste material. It is characterized by a very small microcrack zone at the crack tip (Fig. la), typically of submillimetre scale, low fracture energy of the order of 0.01 kJm -2, and a linear load versus load-point displacement curve from a fracture test. Quasi-brittle fracture can be observed in concrete and in most fibre-reinforced cements or concretes (FRC). It is characterized by a bridging process zone in addition to the small microcrack zone at the crack tip (Fig. lb). The bridging action provides additional energy absorption through aggregate and/or ligament bridging in concrete, and through fibre bridging in FRC, in the wake of the crack front. For quasi-brittle materials the fracture energy extends a large range, from 0.1 kJm -2 in concrete to several kJ m -z in the case of FRC. Correspondingly, the process zone size extends from the mm scale to the cm scale. The load versus load-line displacement curve from a fracture test may involve a small non-linear region near the peak load, with a significant post-peak tension-softening behaviour. Research into quasi-brittle materials in the past decade has been extensive (see, for example [1, 2] for a recent collection of papers on the subject). It must be mentioned that the classification of the fracture characteristics for cementitious materials described above may also be applicable to current monolithic and fibre-reinforced ceramics.

The crack resistance in polybutylene terephthalate (PBT) at crack initiation and during steady crack growth

The resistance to crack initiation and quasi-static crack propagation is investigated for a polybutylene terephthalate (PBT) using annealed and unannealed three-point bend specimens. The resistance to crack initiation (Ri) is determined based on the generalized locus method which determines the resistance to crack growth including crack initiation utilizing the locus of characteristic points on the load against load-point displacement curves of specimens which differ only in initial crack length. This generalized locus method also enables us to investigate the invariance of the crack resistance value along the locus line. The steady state crack resistance (Rp) during quasi-static crack propagation is determined utilizing the functional relation between total essential energy (Uf) for complete fracture and the initial ligament length. The total essential energy is the sum of the blunting energy and the integration of the resistance to crack propagation with respect to the cracking area. The invariance of the crack initiation resistanceRi, and the steady state resistanceRp is discussed based on the experimental results of the annealed and unannealed specimens which show different sizes of crack tip plastic deformation.

Fracture toughness for the specimens with shallow cracks

The relationship between the fracture toughness J i and the crack length/specimen width ratio ( a W ), i.e. J i-( a W ) curve, was investigated by a single specimen method, where the ratio ( a W ) was varied from 0.05 to 0.5 keeping W constant. The fracture initiation was determined by a clip-gauge displacement vs load-point displacement curve method. The J i-( a W ) curve showed that with increasing ratio ( a W ) the J i went up rapidly and then down after it reached the fracture toughness peak (FTP), at last it tended to a constant which was the fracture toughness of the materials in the way of a standard test. The J i values at FTP was about twice as large as that with deep crack specimens. A parameter ( a W ) 0.10 , at which J i was 10% higher than that at a W = 0.5 , was defined to distinguish the shallow and deep cracks. Three regions were divided in the J i-( a W ) curve in order to evaluate the significance of the crack length.

On the resistance to crack initiation and growth

The resistance to crack propagation starting from crack initiation to complete fracture is discussed. A method which determines crack growth resistance utilizing the locus of any set of characteristic points on the load vs load-point displacement curves of specimens which differ only in initial crack length is presented. This generalized locus method can also be used to investigate the invariance of the crack resistance along any set of characteristic points. Experimental evaluation of the crack resistance from crack initiation to steady state propagation is performed using a polymeric material. The resistance to crack initiation is determined in terms of the critical J- integral value ( J c ). The resistance to crack propagation at maximum load point is also investigated utilizing the locus of the maximum load points on the load-displacement curves. The plateau resistance ( R p ) during extensive crack propagation is determined utilizing the total essential energy for a complete fracture which is the sum of the blunting energy and the integration of the resistance to crack propagation with respect to the cracking area. The experimental result supports the assumption that the crack initiation resistance ( J c ) and the plateau resistance ( R p ) values are invariant regardless of the initial crack length provided the irreversible deformation zone size around the crack tip is not confined by specimen geometry.

On the determination of fracture toughness in polymers

A method for finding the critical J-integral value, J c, utilizing the locus line of crack initiation points, is found to be useful in determining the fracture toughness of polystyrene (PS), modified polymethylmethacrylate (PMMA), and polypropylene (PP) homopolymer. This method is also shown to be useful in determining the fracture energy at other critical points, such as the maximum load points which can occur in the nonlinear region of the load and load-point displacement curves. A theoretical equation for the calibration factor Φ for linear elastic materials is utilized in determining J c values of polycarbonate (PC), nylon, and vinyl ester from a single test specimen. The critical J-integral values calculated using Φ or based on the locus line of crack initiation points which occurred in a fairly linear elastic range are compared with the values obtained using the critical stress intensity factor K c.

Analytical study of J estimation formulas for three-point bend specimen.

Rice has shown a simplified method for estimating the J-integral of a deeply cracked bend bar, that is J==2U/Bb where U is the area under the load versus the load point displacement curve, B is the specimen thickness and b is the remaining ligament. It has not been made clear, however, how deep is a deep enough crack for finite size specimens. In this study, an applicable range of the Rice formula for the three-point bend specimen used in the elastic-plastic fracture toughness JIC test is studied analytically. The Rice formula is compared directly with the definition of J as a change in potential energy. Results show that an assumption of a deep crack is required only for a linear elastic material and is not required necessarily for a rigid perfectly-plastic material. In order to obtain the quantitative data, the conditional equation is calculated numerically by varying the crack length for three materials; linear elastic, rigid perfectly-plastic and elastic perfectly-plastic. Results show that the Rice formula is valid when a/W≳0.4 for a linear elastic material. Based on the results, a recommended precrack length of the three-point bend specimen in the JIC test is newly proposed.

Evaluation of theJIntegral for the Compact Specimen

AbstractMethods for determining the J integral from an experimental load versus load point displacement curve for the compact specimen are discussed. The original analysis by Merkle and Corten, which accounted for the tension component in the compact specimen, is presented along with a simplified version (of the analysis) that is shown to be essentially equivalent to the original formulation. Based on experimental results from Landes, Walker, and Clarke, a further simplified expression is recommended as the best expression to use for determining J for the compact specimen.

Application of the (lanteigne) plastic zone correction in elastic-plastic fracture

where K, is the stress intensity factor, a is a coefficient which depend on plane stress or plane strain conditions, a, is the yield strength and A,, Al.. . are given in terms of the coefficients ol, 02. . . of Westergaard[2] for a crack in an infinite elastic plate. A method for evaluation of yy for compact tensile specimens has been described and its use to obtain a value of the J-integral, namely JrC, under controlled loading conditions using a single specimen has been reported[3]. In Ref. [3], ‘yy was obtained experimentally for a tool steel, 06, in the as-received condition. This material exhibited an elastic-plastic fracture behavior as evident from the load against load point displacement curves obtained. In this investigation, the plastic zone correction yy was obtained for four steels which also exhibit an elastic-plastic fracture behavior in the conditions under which they were tested. The results confirm that the plastic zone correction yy produces an improved reproduction of the experimental data. Because three point bending specimens were used in this investigation, a modification of the procedure described in Ref. [3] is necessary. If the total load point displacement is expressed as,