A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints – Part I: Experiments

The effect of bondline thickness, from 130 μm to 790 μm, on the fatigue and quasi-static fracture behavior of aluminum joints bonded using a toughened epoxy adhesive was studied experimentally under mode-I (DCB) and mixed-mode (ADCB) loading. Under mode-I loading, it was found that the fatigue threshold energy release rate, G_th, decreased for very thin bondlines, while under mixed-mode loading, the G_th changed very little with bondline thickness. In both cases, the effect of bondline thickness was more pronounced at higher crack growth rates. For quasi-static fracture, the effect of adhesive thickness on the energy release rate for the onset of fracture from the fatigue threshold, G_c0, was similar to that found for the fatigue threshold; however, the steady-state energy release rate, , increased linearly with increasing bondline thickness.     

Fracture toughness and hydrogen embrittlement of pipes with notches

A technique for experimental determination of fracture toughness and hydrogen embrittlement of pipes made of API 5L X52 steel is described. The tests were performed using arc-shaped specimens with a notch cut out from pipes under the conditions of a three-point bend. The fracture toughness was determined in terms of the J-integral and the stress intensity factor at the notch tip. The value of K _ρ,c was established using the volumetric method based on the experimentally measured critical load and the results of the FEM calculation of the distribution of elastic-plastic stresses ahead of the notch tip, and J _ρ,c was determined using the method of separable functions. The effect of hydrogen embrittlement was studied using electrolytically prehydrogenated specimens.     

A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

Multiscale simulation of fracture of braided composites via repetitive unit cells

Two-dimensional triaxially braided composites (2DTBCs) are attractive in crashworthiness design because their fracture can dissipate a significantly larger amount of impact energy than other light-weight materials. This paper aims at predicting the fracture energy, G_f, and the effective length of the fracture process zone, c_f, of 2DTBC composites. Since the fracture parameters are best manifested in the scaling properties and are the main parameters in the size effect law, the nominal strengths of three geometrically similar notched beams of three different sizes are simulated in a 3D finite element framework. The simulations are run for three different bias tow angles: 30°, 45° and 60°. Continuum beam elements in front of the notch are replaced with repetitive unit cells (RUCs), which represent the 2DTBC’s mesostructure, and are located in the region of potential cracking. Multiscale simulations, incorporating damage mechanics, are used to predict the pre- and post-peak response from three-point bending tests. Nominal stresses are calculated from the predicted peak loads and used to fit the size effect law. The dimensionless energy release rate function g(α) is determined from the J-integral. The values of G_f and c_f are then determined using g(α) and the size effect law. With some exceptions, the results in general match well with the results of size effect experiments, and particularly the strong size effect observed in the tests.     

Relationship between fracture parameters from two parameter fracture model and from size effect model

This paper studies the relationship between the two parameter fracture model and the size effect model. An equivalency between two models is first established based on infinitely large size specimens. Based on this equivalency, relationships between material fracture parameters (K _Ic ^s , CTOD_c) and (G _f, c_f) are derived. Using these relationships, values of (K _Ic ^s , CTOD_c) and (G _f, c_f) can be predicted from each other. It is found that the relationship betweenCTOD _c andc _f theoretically depends on both specimen geometry and initial crack length. However this dependency is numerically insignificant, except for tensile plate with a short center notch. The obtained results may explain why both the two parameter fracture model and the size effect model can reasonably predict fracture behavior of quasi-brittle materials.     

Toughness and microscopic fracture mechanisms of unfilled and short-glass-fibre-filled poly(cyano arylether)

Fracture mechanisms of an advanced high-strength thermoplastic poly(cyano arylether) (PCAE) and its short-glass-fibre (SGF)-reinforced composites have been studied in relation to toughnesses K _c and J _c. Test temperatures were 23 and 100 °C. Reflected and transmitted optical observations were combined with scanning electron microscopy for the fractographic investigation. For unreinforced PCAE tested at 100 °C, the damage area in front of a notch becomes fairly large in size and consists of numerous tensile microfailures around the local plastic yielding zone, as compared with that tested at 23 °C. This resulted in a substantial improvement of K _c and a big increase in J _c. Filling fibres, however, produced both toughening and anti-toughening results: effects of fibre spanning, pull-out and bridging across the local plastic failure zone and zigzag propagation of fracture due to fibre filling, improved the toughness. However, adhesive failure at the fibre-matrix interface, tensile microcleavage at the fibre ends and straightforward fracture in the skin layer, considerably diminished the values of K _c and J _c, except for the trend of K _c at 23 °C.     

Two-parameter fracture criterion (Kρ,c-Tef,c) based on notch fracture mechanics

A two-parameter fracture criterion has been proposed to predict fracture conditions of notched components. This criterion includes the critical notch stress intensity factor K _ρ,c , which represents fracture toughness of a material with a notch of radius ρ, and the effective T-stress. The effective T-stress T _ef has been estimated as the average value of the T-stress distribution in the region ahead of the notch tip at the effective distance X _ef . These parameters were derived from the volumetric method of notch fracture mechanics. The results of numerical T _ef,c -stress estimation are compared to the T _ef,c -stress results obtained from experimental analysis. The material failure curve or master curve K _ρ,c = f(T _ef,c ) has been established as a result of the notched specimen tests. A large T _ef,c range was covered from −0.80 σ _Y to +0.19 σ _Y using SENT, CT, RT (roman tile) and DCB specimens. It was shown that the notch fracture toughness is a linear decreasing function of the T _ef,c -stress. The use of the material failure curve to predict fracture conditions was demonstrated on gas pipes with the surface notch.     

Impact properties of polyurethane and glass fibres reinforced composites

Impact resistance of the polyurethane matrix and composites with glass fibres of various volume fractions was investigated. The theory of linear elastic fracture mechanics (LEFM) was successfully applied to obtain a quantitative assessment of a parameter of toughness, the critical strain energy release rate (G _c), which was determined from the energy (W ^*) required to fracture sharply-notched specimens by taking into account specimen dimensions and notch depth. It is found that the G ^* is not a linear function of reinforcement concentration. The impact resistance with low volume fraction _f=0.045 of glass fibres decreases as compared to that of the matrix. However, with further incorporation of glass fibres, the impact resistance gradually increases, reaching its maximum for the volume fraction _f=0.158. An explanation of this non-linear behaviour is provided in this paper.     

Influence of moisture and resin ductility on delamination

The critical strain energy release rate, $\text{G}{}_{\mathrm{c}}$, at edge delamination has been measured indirectly for angle-ply laminates with standard resin and toughened resin under mixed-mode loading at various K_III/K_I ratios. It is shown that $\text{G}{}_{\mathrm{c}}$ increases with increasing K_III/K_I ratio. The critical energy release rate is significantly higher in the toughened resin laminate than in the standard resin laminate. Moisture absorption does not affect the critical energy release rate for laminates with standard resin, whereas it reduces the critical energy release rate for laminates with toughened resin. In confirmation of this, it has been observed that the hackle-dominated brittle resin fracture occurring in the standard resin laminate is replaced by semi-ductile fracture in the toughened resin laminate. When the toughened resin laminate is moisturized prior to testing the fracture surface appearance returns to being hackle-dominated.     

TOUGHNESS GIVEN BY ACCUMULATED WORK IN LEFM: POSSIBLE IMPLICATIONS FOR ELASTOPLASTIC JR"RESISTANCE CURVES"

Abstract J _R vs. Δa curves are often determined from the accumulated work U_acc operated on by an η/Bb factor, and rising J_R curves are said to indicate increased resistance to fracture. It seems to have been overlooked, however, that Krafft G_R resistance curves in lefm are not obtained in this way from U_acc. Indeed the concept of accumulated work during propagation does not appear in the lefm literature. This paper investigates U_acc in lefm and derives relations for ηU_acc/Bb vs. Δa/b for the compact tension and 3-point notched bend testpieces. For fracture at constant G_c a series of quasi-linear plots is predicted: all have G_c as their ordinate intercept with slopes which are multiples of G_c, individual values depending on the starting (a/W). Note that ηU_acc/Bb does not indicate current toughness directly during globally-elastic crack propagation; the ordinate values not coinciding with the known toughness G_c (or R, K_c etc) even in cases where there is “real”G_R behaviour in the Irwin-Krafft sense.     

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, _J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J _d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J _d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.     

Fracture characterization of short glass fibre reinforced thermoplastic polyester by theJ-integral

Fracture initiation of short glass fibre reinforced thermoplastic polyester was characterized by theJ-integral measurement based on the energy release rate interpretation ofJ. The criticalJ value (J _c) is shown to be a fracture characterizing parameter for the onset of the crack initiation in the injection moulded short glass fibre reinforced composite material. TheJ _c value of the composite is estimated by be 6.0kJ m^–2. This value is in good agreement with the linear elastic strain energy release rate (G _c), since the composite exhibited a fairly linear stress-strain relationship. The estimated ratios ofJ _c to the total energy absorbed per unit uncracked area are in good agreement with the analytically obtained values after the remote energy dissipation due to fibre and matrix interaction away from the crack tip has been subtracted from the total energy.Nomenclature J J-integral - J _c The criticalJ - G Elastic strain energy release rate - G _c The criticalG - K _l Opening mode stress intensity factor - The criticalK _l - P Applied load - x Load-point displacement - B Specimen thickness - E Young's modulus - v Poisson's ratio - F Force - Y Central deflection - a/W Ratio of the crack length to the specimen width - _y Yield stress - U _t Total strain energy in loading a specimen - U _d Remotely dissipated strain energy after unloading - U _t–d U _t–U _d - _t Ratio ofJ _c toU _t per unit uncracked ligament - _t–d Ratio ofJ _c toU _t–d per unit uncracked ligament.     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Crack velocity dependence of longitudinal fracture in bone

An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G _c) and critical stress intensity factor (K _c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10^–5 m sec^–1 produced increases in G _c (from 1736 to 2796 J m^–2), K _c (from 4.46 to 5.38 MN m^–3/2) and W. At crack velocities >23.6×10^–5 m sec^–1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec^–1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.     

Failure mechanics in ternary composites of polypropylene with inorganic fillers and elastomer inclusions

The effects of phase morphology, interfacial adhesion and filler particle shape and volume fraction on the fracture toughness of polypropylene (PP) filled with CaCO₃ or Mg(OH)₂ and ethylene-propylene elastomer (EPR) were investigated. Separation of the inorganic filler and elastomer particles was achieved using maleic-anhydride-grafted PP (MPP) to enhance the inorganic filler-matrix adhesion. Encapsulation of the rigid filler by the elastomer was achieved by using maleic-anhydride-grafted EPR (MEPR) to increase the inorganic filler-elastomer adhesion. The two limiting morphologies differed significantly in fracture toughness under impact loading at the same material composition. A model for a mixed mode of failure, accounting for the plane strain and plane stress contributions to the strain energy release rate,G _c, was used to predict the upper and lower limits forG _c for the two limiting morphologies over an interval of elastomer volume fractions,v _e, from 0–0.2 at a constant filler volume fraction,V _f = 0.3, and over the filler volume fraction from 0–0.4 at constant EPR content. The role of material yield strength in controlling fracture toughness has been described successfully using Irwin's analysis of plastic zone size. The presence of elastomer enhances both the critical strain energy release rate for crack initiation,G _c, and the resistance to crack propagation as expressed by Charpy notched impact strength for the two limiting morphologies. Satisfactory agreement was found between the experimental data and predictions of upper and lowerG _c limits.     

Mixed-mode fracture load prediction in lead-free solder joints

Double cantilever beam (DCB) fracture specimens were made by joining copper bars with both continuous and discrete SAC305 solder layers of different lengths under standard surface mount (SMT) processing conditions. The specimens were then fractured under mode-I and various mixed-mode loading conditions. The loads corresponding to crack initiation in the continuous joints were used to calculate the critical strain energy release rate, J_ci, at the various mode ratios using elastic–plastic finite element analysis (FEA). It was found that the J_ci from the continuous joint DCBs provided a lower bound strength prediction for discrete 2 mm and 5 mm long joints at the various mode ratios. Additionally, these J_ci values calculated from FEA using the measured fracture loads agreed reasonably with J_ci estimated from measured crack opening displacements at crack initiation in both the continuous and discrete joints. Therefore, the critical strain energy release rate as a function of the mode ratio of loading is a promising fracture criterion that can be used to predict the strength of solder joints of arbitrary geometry subject to combined tensile and shear loads.     

J andG canalysis of the tearing of a highly ductile polymer

The use of a conventionalJ analysis to describe the ductile tearing of thin low density polyethylene sheet is described. This is a measure of the total energy required to cause fracture. The use of the current energy release rate to determine the local dissipation rate is then given and it is shown that an initiation (plane strain) and reasonably constant propagation (plane stress) values are obtained. Input energy of system - A Area of specimen - B Thickness of specimen - W Width of specimen - a Crack length - J J-integral - G _c Energy release rate - P Load - U Energy - C Compliance - M Constraint factor - _y Yield stress - u Displacement - Dimensionless factor     

Fracture toughness and absorbed energy measurements in impact tests on brittle materials

Previous work on impact testing has shown that the energy/unit area (w) normally measured in notched impact tests is dependent on specimen geometry. A fracture mechanical analysis has now been developed to account for the observed dependence ofw on notch size. A correction factor () has been derived to accommodate notch effects and this allows for the calculation of the strain energy release-rateG directly from the measured fracture energies.Tests on PMMA have shown that corrected results are independent of specimen geometry and theG _c for PMMA has been evaluated as 1.04 × 10³ J m^–2. The experimental results show that there is an additional energy term which must be accounted for and this has been interpreted here as being due to kinetic energy losses in the specimens. A conservation of momentum analysis has allowed a realistic correction term to be calculated to include kinetic energy effects and the normalized experimental results show complete consistency between all the geometries used in the test series.It is concluded that the analysis resolves many of the difficulties associated with notched impact testing and provides for the calculation of realistic fracture toughness parameters.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.