On the fundamental basis of fracture mechanics

Based on the crack tip stress and strain fields, the linear and the non-linear fracture mechanics have been developed. Their applications to the studies of fracture initiation and stable crack growth may differ because of the difference in the basic postulates of various fracture theories. The correct postulates will help to develop non-linear fracture mechanics for valid fracture toughness measurements and to extend fracture mechanics beyond the realms of K and J.The basic postulates of the linear elastic fracture mechanics are examined. The theory of global energy balance, the theory of sharp notch, and the theory of the characterization of crack tip stress and strain fields by K are analyzed. Fracture initiation and stable crack growth are local fracture phenomena. Therefore the global energy balance theory for crack initiation and stable crack growth without the study of the detailed fracture processes is fortuitous. The capability of the stress intensity factor to characterize the crack tip stress and strain fields for the localized fracture process is the basis for the validity of the linear elastic fracture mechanics.The concept of the characteristic crack tip field can be directly extended to the non-linear fracture mechanics. The fracture toughness and the tearing modulus of a tough material are measures of the fracture ductility of the material. The possibility to extend fracture mechanics beyond the realms of K and J are discussed.     

The measurements of fracture toughness of ductile materials

Near tip strain is proposed as a ductile fracture criterion. This criterion was used to study the onset of slow growth of surface crack. The data from two batches, B and C, of fully annealed 2024-0 aluminum alloy and HY-80 steel substantiated the proposed criterion. The measured fracture toughness at the onset of surface crack growth are 280, 110 and 800 ksi √in. for these three materials respectively. It was demonstrated that the measurement can be made easily with a small foil resistance strain gage. The near tip strain criterion was compared with both crack surface opening displacement and J-integral criteria.     

Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

Application of finite element method for determination of stress intensity factor and plastic zone geometry in an aluminium alloy sheet under uniaxial tension

High strength materials have gained prominence in the fields of aero-structures, space missiles, ship-building, pressure vessels etc. However, high strength materials are often characterised by low values of crack resistance or fracture toughness. Knowledge of stress intensity factor (SIF) is essential to predict their fracture toughness. SIF values can be obtained both theoretically and experimentally. Theoretical methods include analytical techniques as well as the finite element method (FEM). The former is used for simpler geometries and the latter for complicated geometries of engineering structures. The SIF as a function of crack size in an aluminium alloy 2024-T₃ (Al-4·5% Cu, 1·5% Mg, 0·6% Mn) sheet was determined by a computer method. These values were obtained directly from the stresses as well as indirectly from strain energy release rateG andJ integral. The results agree well with the normalised values obtained from an ASTM formula. The size and shape of the plastic zone at the crack tip have been determined as a function of nominal stress for a fixed crack length. The plastic zone has the form of two ellipsoids with their maximum spreads oriented around 69° to the crack axis.     

Rate-dependent fracture toughness of pure polycrystalline ice

A series of three-point bend tests using single edge notched testpieces of pure polycrystalline ice have been performed at three different temperatures (–20°C, –30°C and –40°C). The displacement rate was varied from 1 mm/min to 100 mm/min, producing the crack tip strain rates from about 10^–3 to 10^–1 s^–1. The results show that (a) the fracture toughness of pure polycrystalline ice given by the critical stress intensity factor (K _IC) is much lower than that measured from the J—integral under identical conditions; (b) from the determination of K _IC, the fracture toughness of pure polycrystalline ice decreases with increasing strain rate and there is good power law relationship between them; (c) from the measurement of the J—integral, a different tendency was appeared: when the crack tip strain rate exceeds a critical value of 6 × 10^–3 s^–1, the fracture toughness is almost constant but when the crack tip strain rate is less than this value, the fracture toughness increases with decreasing crack tip strain rate. Re-examination of the mechanisms of rate-dependent fracture toughness of pure polycrystalline ice shows that the effect of strain rate is related not only to the blunting of crack tips due to plasticity, creep and stress relaxation but also to the nucleation and growth of microcracks in the specimen.     

A numerical investigation on the geometry dependence of the crack growth resistance in CT specimens

The influence of the specimen thickness B and the ligament length b on the J _R -curves is numerically investigated for CT specimens. The thickness effect is taken into account with 2-D analyses by dividing a plain sided specimen into a plane stress part and a plane strain part. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement for crack growth initiation (CTOD_i) and the crack tip opening angle for stable crack growth (CTOA_C). It is shown that for the global behaviour of a plain sided specimen, the B/b ratio is essential. The difference between the geometry dependence of the initiation value of the J-integral and the geometry dependence of the slope of the J _R -curves is also shown.     

High rate toughness of ductile polymers

Impact toughness of two highly ductile polymers: acrylonitrile-butadiene-styrene (ABS) terpolymer and polypropylene block copolymer (PPBC) - was evaluated using the essential work of fracture (EWF) - and a J-R resistance single specimen curve - S_pb techniques. The EWF has proved to be capable of determining toughness from the total fracture energy of several samples differing in initial ligament length and the linear regression of the data. On the other hand, the S_pb method, which is based on the load separation principle, is able of constructing J-R curves by inferring instantaneous crack growth length from the sole comparison between one sharp and one blunt-notched load-displacement traces. Results show that both methodologies can be used under impact conditions when evaluating ABS polymers. However, ABS impact fracture toughness value yielded by the EWF method, w_Ie, was larger than the J_0.2 value obtained from the S_pb method. This difference was imputed to the more progressive development of the necking zone in front of the crack tip under plane strain conditions. On the contrary, for very ductile fracture behavior like that demonstrated by PPBC in which J-controlled conditions were not achieved and hence J-R curves could not be built the EWF appeared as a valuable alternative to characterize impact toughness.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.     

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.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

The influence of weld strength mismatch on crack-tip constraint in single edge notch bend specimens

Previous work by Dodds and Anderson provides a framework to quantify finite size and crack depth effects on cleavage fracture toughness when failure occurs at deformation levels where J no longer uniquely describes the state of stresses and strains in the vicinity of the crack tip. Size effects on cleavage fracture are quantified by defining a value termed J _SSY: the J to which an infinite body must be loaded to achieve the same likelihood of cleavage fracture as in a finite body. In weld metal fracture toughness testing, mismatch between weld metal and baseplate strength can alter deformation patterns, which complicate size and crack depth effects on cleavage fracture toughness. This study demonstrates that there is virtually no effect of ±20 percent mismatch on J _SSYif the distance from the crack tip to the weld/plate interface (L _min) exceeds 5 mm. At higher levels of overmatch (50 to 100%), it is no longer possible to parameterize the departure of J _SSYfor a weldment from that for a homogeneous SE(B) based on L _min alone. Weld geometry significantly influences the accuracy with which J _SSYfor a welded SE(B) can be approximated by J _SSYfor a homogeneous specimen at these extreme overmatch levels.     

Calculation of the energy J-integral for bodies with notches and cracks

The approximate solutions for calculation of the energy J-integral of a body both with a notch and with a crack under elastic-plastic loading have been obtained. The crack is considered as the limit case of a sharp notch. The method is based on stress concentration analysis near a notch/crack tip and the modified Neuber's approach. The HRR-model and the method based on an equation of equilibrium were also employed to calculate the J-integral. The influence of the strain hardening exponent on the J-integral is discussed. New aspects of the two-parameter J ^* _c-fracture criterion for a body with a short crack are studied. A theoretical investigation of the effect of the applied critical stress (or the crack length) on the strain fields ahead of the crack tip has been carried out.     

Analysis of low temperature impact fracture data of thermoplastic polymers making use of an inverse methodology

In this work room and low temperature impact fracture data toughness of rubber modified polypropylene, polyethylene and rubber toughened polymethylmetacrylate have been assessed. In order to minimize the well-known dynamic effects a previously developed inverse methodology was used to treat force-time traces. Fracture parameters, such as K_IQ and J_C were estimated and the benefits of the inverse methodology were evaluated. The suitableness of energetic and force based toughness parameters for estimating a brittle to ductile transition was evaluated. The employment of the inverse methodology allowed us to infer the values of the crack tip loading rate, dK/dt, without the need of cushioning.     

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J ₂ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.     

Fracture behaviour of dynamically loaded ship building plate material

The fracture toughness values of ship building mild steel measured over a temperature range ? 196°C to 28°C and crack tip strain rates ranging from 10^?5/sec to 10^?1/sec are examined in the light of the models recently proposed by Malkin and Tetelman. The effect of a change in inclusion morphology brought about by electroslag refining on the fracture toughness of the steel is also evaluated. It is found that the stress-induced fracture criterion ofthe model applies for the case where the ratio $\text{σ}{}^1{}_{\mathrm{f}}\text{σ}{}_{\mathrm{YS}}\text{? 3.94}$. This ratio is independent of the strain rate. In the strain induced fracture region of the model, the critical strain near the crack tip, ?_f(Rβ) is a function of the yield stress irrespective of temperature and strain rate. Electroslag refining reduces significantly the size and volume fraction of the inclusions and changes their shape from prolate ellipsoid to spherical. Apparently the electroslag refining does not improve fracture toughness significantly if the fracture toughness of the as received material measured with the major axis of the inclusions perpendicular to the crack front, is taken as a basis of comparison.     

Influence of notch root radius on ductile rupture fracture toughness evaluation with Charpy-V type specimens

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρ_eff) below which applied J-intergral values at fracture initiation are constant. These ρ_eff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρ_eff.     

Influence of specimen size and microstructure on the fracture toughness of a martensitic stainless steel

The fracture toughness of alloy HT-9,² a martensitic stainless steel under consideration for fast reactor and fusion reactor applications, was determined from circular compact tension specimens using the multi-specimen R-curve method. Specimens with thicknesses of 11.94, 7.62 and 2.54mm and widths of 23.88 and 11.94 mm were tested to investigate the effects of specimen size on fracture toughness. The test results obtained from all specimens are in good agreement and thickness requirements for a valid J_1c test are satisfied. The experiment indicates that small specimens of HT-9 may be used for post-irradiation fracture toughness testing.Fractographic examination of the fracture surfaces reveals that fracture in HT-9 is significantly influenced by delta ferrite stringers present in the material. The fracture surface examination and crack opening displacement measurements for specimens tested at various temperatures are consistent with the temperature dependence of the J_1c results.     

A finite element analysis of plane strain dynamic crack growth at a ductile-brittle interface

In this work, steady, dynamic crack growth under plane strain, small-scale yielding conditions along a ductile-brittle interface is analysed using a finite element procedure. The ductile solid is taken to obey the J ₂ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behaviour. The objectives of this work are to establish the validity of an asymptotic solution for this problem which has been derived recently [12], and to examine the effect of changing the remote (elastic) mode-mixity on the near-tip fields. Also, the influence of crack speed on the stress fields and crack opening profiles near the propagating interface crack tip is assessed for various bi-material combinations. Finally, theoretical predictions are made for the variation of the dynamic fracture toughness with crack speed for crack growth under a predominantly tensile mode along ductile-brittle interfaces. Attention is focused on the effect of mismatch in stiffness and density of the constituent phases on the above aspects.