J II fracture testing of a plastically deforming material

A compact model II fracture specimen was previously analyzed and employed to determine the mode II fracture toughness K _IIc , of perspex. In employing this specimen for a more ductile material such as aluminium, it was observed that the load vs. crack sliding displacement record becomes nonlinear for small loads. Thus, concepts of linear elastic fracture mechanics cannot be employed. To this end, the specimen was calibrated for J-integral testing, so that J _IIc mesurements can be performed.In this study, mode I and II tests are carried out on an aircraft aluminium alloy, AI 7075-T7351. First, standard K _Ic tests are performed leading to a value of 27.9 15-1 which would be equivalent to a J _Ic of 10.7 kN/m. Then standard J _Ic tests are carried out on this material with specimen thicknesses, of 5, 7.5 and 9.9 mm, leading to an average J _Ic value of 10.5 kN/m. Methods for J _II testing are proposed; a series of specimens of six thicknesses between 5 and 16 mm are employed for testing. An average J _IIc value was found to be 40.2 kN/m which yields a K _IIc value of 54.1 15-2. Thus, K _IIc is seen to be approximately twice that of K _Ic for this material.     

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (K_I(t) for opening mode I, and K_II(t) for sliding mode II), mode mixture ratio (K_I(t)/K_II(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (K_Id and K_IId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ?50 mm specimen, however it is 10° for the ?130 mm and ?200 mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. K_IId is generally greater than K_Id. Both K_Id and K_IId increase with increment of specimen size, and this trend for K_IId is more remarkable than that for K_Id.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

Study on the behavior of elastic-plastic fracture under mixed I+II mode loading in aluminum alloy Ly12-J-integral analysis

The elastic-plastic fracture behavior of aluminum alloy Ly12 under mixed I+II mode loading was studied by finite element method and fracture test. A mixed mode elastic-plastic fracture criterion of J-integral was proposed by using the J-resistance curve, and the maximum fracture effective plastic strain _p max of different mixed ratios at crack tip were also calculated. The results show that(1) the initiation J-integral values of different mixed ratios have the equation

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.     

J integral and COD fracture criteria in 40CrNiMo steel under mixed mode I+II loading

Abstract

By defining the J integral and crack opening displacement (COD) under mixed mode I + II loading, a mixed J integral fracture criterion is proposed and the relationship between the J integral and COD in 40CrNiMo steel is discussed. The mixed J integral J _M and its mode I and II components J _I and J _II were calculated by the finite element method, while the mixed COD and its mode I and II components CTOD and CTSD were measured using a duplicated grid. The critical values J _Mc and COD_c for mixed crack initiation were determined by a resistance curve. The results show that mode II loading lowers both J _Mc and COD_c for 40CrNiMo steel. The variation of J _Mcfrommode I tomode II loading is found to be in accordance with the linked equations J _Mc=J _Ii+J _IIi;(J _Ii/J _Ic)+(J _IIi/J _IIc)=1, where J _Icand J _IIcare the critical J integrals of pure mode I and II cracks,and J _Iiand J _IIiare the mode I and II components of J _Mc at arbitrary mixed K_I/K_II ratio respectively; the J _Mc value for a given K_I/K_II ratio can be obtained if J _Ic and J _IIc are known. Finally, under valid loads, J_M and the mixed COD satisfy the relation J _M=J _I+J _II=dσ₀CTOD+d _sτ₀CTSD. When unified by yield stress σ_y the relation becomes J _M=dσ_yCOD, where d _n, d _s and d are coefficients, and σ₀ and τ₀ are the tensile and shear stress at the crack tip strip respectively. While d _n and d _s vary with K_I/K_II ratio and materials, d was found to have a constant value of about 0.98.     

An insight into mode II fracture toughness testing using SCB specimen

The effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors K_I and K_II but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.     

The behaviour of cracks in elastic-plastic materials under plane normal and shear loadings

Cracks in structures are often subjected to complex loading conditions. The direction of the crack extension depends on the normal and the shear components of the load. This paper is based on the kinking behaviour of cracks taking elastic-plastic behaviour of materials into account. The J-integral and the mixed-mode components J _I and J _II were determined after having performed several finite element analyses for different loading conditions. The path independence of J, J _I and J II is investigated for both, the line integral proposed by Rice and the volume integral proposed by deLorenzi. For correctly determined crack deflection angles the J _II-component vanishes when a FE-model with a kinked crack is considered. Hence, cracks propagate perpendicularly to the local mode I load.     

Alternative test method for interlaminar fracture toughness of composites

Two methods of determining the mode I interlaminar fracture toughness for fiber-reinforced polymer matrix (FRPM) composites using a double cantilever beam (DCB) test are compared. The standard method of determining G _IC is based in linear-elastic fracture mechanics theory and requires a visual measurement of the crack length, presenting data acquisition and analysis difficulties. The proposed method makes use of elastic–plastic fracture mechanics theory and an analytical closed form solution to the J-integral to relate the fracture toughness J _IC , load, and angular displacement at the load application points. This method has the advantage of replacing visually acquired data with data easily obtained using inexpensive transducers as well as being applicable to a broader class of materials.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials

The centrally cracked Brazilian disc specimen has been used frequently in the past for investigating mixed mode I-II fracture toughness in rock materials. However, a review of the available test results reveals that the conventional fracture criteria like the maximum tangential stress criterion always underestimate the mixed mode I-II fracture toughness data obtained from the Brazilian disc specimen. In this paper, a generalized maximum tangential stress criterion which takes into account the effects of the three fracture parameters K_I, K_II and T-stress is used for predicting the mixed mode fracture toughness data available in the literature for several types of rock materials tested with the Brazilian disc specimen. It is shown that the generalized maximum tangential stress criterion provides significantly improved predictions for the experimental results.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Characterization of fracture toughness of high strength low alloy steel weldments using stretch zone width measurements

Most of the industrial applications involving use of high-strength low-alloy steels require good weldability. Thus it is important to characterize the properties of the welded steels, especially the heat affected zone. Attempts have been made to characterize the fracture toughness of the HAZ by the use of theJ-integral and the crack opening displacement. In the present study, the effect of addition of titanium, vanadium and niobium, as well as combinations of these, on the fracture toughness of the heat affected zone of welded steel plates is examined. Six compositions were used in this study. Three-point bending specimens as well as tensile specimens were prepared. The fracture surfaces were examined in a scanning electron microscope to determine the fracture mode as well as the extent of the stretch zone as the crack blunts. Calculation of the fracture toughness parameter,J _lc, is carried out through a quantitative stereofractographic analysis of the stretch zone at the crack tip. The results show that there is a marked increase inJ _lc due to the addition of the various alloying elements. Generally, the addition of niobium and titanium alone produce the highestJ _lc due to the extent of grain refinement that these elements produce.     

Fracture mechanics analysis of anisotropic plates by the boundary element method

This paper presents an analysis of mixed mode fracture mechanics problems arising in anisotropic composite laminates. The boundary element method (BEM) and the J _k integral are presented as accurate techniques to compute the stress intensity factors K _I and K _II of two dimensional anisotropic bodies. Using function of a complex variable a decoupling procedure is derived to obtain the stress intensity factors. The procedure is based on the computation of the J ₁-integral and of the ratio of relative displacements at the crack faces, near the crack tip. Applications are presented for unidirectional and symmetric laminates of glass, boron and graphite-epoxy materials. Numerical examples of problems of pure mode I and mixed mode deformations are given, in order to demonstrate the accuracy of the method.     

Calculation of the crack tip parameters in the holed‐cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading

In this paper, the crack tip parameters including the stress intensity factors (K_I and K_II), T‐stress and the third terms of the stress field (A₃ and B₃) are determined comprehensively for a disk‐type sample named holed‐cracked flattened Brazilian disk (HCFBD) under various combinations of mode I and mode II loading. The HCFBD specimen is a circular disk containing a central hole in which the initial cracks are created radially from the hole circumference. Moreover, the ends of HCFBD are flattened for the sake of convenient loading. Performing enormous finite element analyses and calculating the stress intensity factors K_I and K_II, the states of pure mode II are determined for different configurations of HCFBD. Furthermore, the sign and magnitude of parameter A₃ which plays an important role to justify the geometry and size effects on the fracture toughness of quasi‐brittle materials are also determined for HCFBD with different geometrical ratios.     

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.     

The effects of ferrrite grain size on fracture of low carbon steel under mixed modes I and II

In the previous article a new methodology is proposed for the study on fracture criterion for the notched or cracked specimens under mixed Modes I and II. In this methodology, any value of K_II/K_I can be applied to the thin-walled hollow cylindrical specimen with notch or crack, the length of which is perpendicular to the specimen axis. Thus the data can be obtained covering all values of K_II/K_I ranging from ∝ to 0, that is, from mode II to mode I.Using this method, the experimental studies were carried out on the effects of ferrite grain diameter upon the fracture of low carbon steel under mixed Modes I and II. The experimental results were compared with various fracture criteria hitherto proposed in literatures. The fracture criterion experimentally obtained is a function of ferrite grain diameter and the value of K_II/K_I, at fracture increases with increase of ferrite grain diameter. On the other hand, the overall direction of the crack growth obeys approximately maximum stress criterion or energy momentum tensor criterion, independent of ferrite grain diameter. Furthermore, this also shows that the fracture criterion does not reveal directly overall direction of crack growth. These characteristics are quite similar in trend to those of the unnotched specimens.     

Elasto-plastic analysis of a mode II fracture specimen

An elasto-plastic analysis of a compact mode II fracture specimen is performed. Both an approximate approach with rigid plastic material and a more exact elasto-plastic finite element calculation are carried out. From this analysis, an -factor is determined relating the J-integral to the internal energy measured along the specimen crack faces. It is shown through the finite element computation that it is justifiable to define an -factor. With this result, it is now possible to perform tests on aluminium specimens so as to determine J _IIc.     

Methods for calculating stress intensity factors in anisotropic materials: Part I—z = 0 is a symmetric plane

The problem of a crack in general anisotropic material under LEFM conditions is presented. In Part I, three methods are presented for calculating stress intensity factors for various anisotropic materials in which z = 0 is a plane of symmetry. All of the methods employ the displacement field obtained by means of the finite element method. The first one is known as displacement extrapolation and requires the values of the crack face displacements. The other two are conservative integrals based upon the J-integral. One employs symmetric and asymmetric fields to separate the mode I and II stress intensity factors. The second is the M-integral which also allows for calculation of K_I and K_II separately.All of these methods were originally presented for isotopic materials. Displacement extrapolation and the M-integral are extended for orthotropic and monoclinic materials, whereas the J_I- and J_II-integrals are only extended for orthotropic material in which the crack and material directions coincide. Results are obtained by these methods for several problems appearing in the literature. Good to excellent agreement is found in comparison to published values. New results are obtained for several problems.In Part II, the M-integral is extended for more general anisotropies. In these cases, three-dimensional problems must be solved, requiring a three-dimensional M-integral.     

Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept

An energy dissipation rate concept is employed in conjunction with the J-integral to calculate crack growth resistance of elastic-plastic fracture. Different from Rice’s J-integral, the free energy density is employed in place of the stress working density to define an energy-momentum tensor, which yields that the slightly changed J-integral is path dependent regardless of incremental plasticity and deformational plasticity. The J-integral over the remote contour is split into the plastic influence term and the J _FPZ-integral over the fracture process zone which is an appropriate estimate of the separation work of fracture. Finite element simulations are carried out to predict the plane strain mode I crack growth behavior by an embedded fracture process zone. It can be concluded that J-integral characterization is in essence a stress intensity-based fracture resistance similar to the K criterion of linear elastic fracture, and energy dissipation rate fracture resistance can be taken as an extension of the Griffith criterion to the elastic-plastic fracture.