Comparison of the static and dynamic fracture behaviour of an AE-460 structural steel

The ductile-to-brittle transition curves of a structural steel under low strain rate (static conditions) and impact (dynamic conditions) are compared in this work, and the influence of the geometry of the initial defect that promotes fracture (notch or crack) is evaluated. The toughness of the precracked specimens was characterised by the J-integral parameters obtained at the initiation of the stable crack growth, J_c, and when the unstable fracture takes place, J_u. The different methods used in dynamic tests in order to calculate the dynamic J-integral parameter, J_d, were evaluated. The use of cracked specimens, instead of notched ones, modifies the transition curve to higher temperatures and, finally, the transition temperature shift between static and dynamic test results is also quantified     

Micromechanical analysis of fatigue cracks in cord–rubber composites

Analyses of two different types of cracks due to fatigue of cord–rubber composites is carried out using micromechanical two-dimensional (2D) and three-dimensional (3D) finite element analysis. The fracture parameter, tearing energy (TE)/J-integral that characterizes the severity of crack tip stresses in rubber composites, is computed from the finite element results of stresses and strains. The results obtained are validated with existing analytical methods in the literature. Numerical results of J-integral values are presented for two crack types, and crack sizes under transverse strain and shear strain loading conditions. The results presented illustrate that crack type, loading, and crack size have a strong effect on the values of J-integral. The results of the J-integral should help our understanding in estimating the severity of local failures in cord–rubber composites.     

The values of J-integral within the plastic zone

A study has been conducted to characterize the J-integral within the plastic zone for different strain hardening materials. The relation between the calculated J-integral and plastic energy enclosed by the selected integration contour is explored for different strain hardening materials. The equations between the J-integral and plastic energy around the crack tip for 7075-T651 aluminum alloy and HY-130 steel have been derived. It is shown that the J-integral is path dependent if the selected integration contour goes across the plastic zone. Results also indicated the plastic energy enclosed by the selected integration contour provides the dominant contribution to the J-integral.     

J-integral estimate for biaxially stressed Mode I cracks based on COD strain

This paper proposes a simple equation for evaluating J-integral values for biaxially stressed Mode I cracks. Finite element analyses were carried out to obtain the relationship between J-integral and crack opening displacement by varying the inelastic constitutive relationship, crack length and stress/strain biaxiality. A quantitative relationship was derived between the J-integral and crack opening displacement for various kinds of stress–strain relationships. A new equation for estimating the J-integral was proposed based on the crack opening displacement. The equation evaluated J-integral values for biaxially stressed Mode I cracks within a 25% error if the yield stress, strain hardening coefficient and exponent were known.     

Cyclic AE count rate and crack growth rate under low cycle fatigue fracture loading

In the low cycle fatigue fracture testing with KS (or JIS) SS41 steel, crack growth rate, AE count rate and J-integral range are measured to get empirical relationships between crack growth rate and J-integral range, AE count rate and J-integral range as well as AE count rate and crack growth rate. All the relationships are shown to be linear on the log—log graphs. It is also shown that the linear relationships can be formulated by using Dunegan's assumption and elastic-plastic fracture mechanics along with the well-known relationships of crack growth rate and J-integral range. It is concluded that the differences between experimental and theoretical values are due to the problem of Dunegan's assumption.     

Determination of J–R curves of thermoplastic starch composites containing crossed quasi-unidirectional flax fiber reinforcement

Thermoplastic starch (MaterBi) composites reinforced with quasi-unidirectional flax fiber in cross-ply (CP) arrangement were produced by film stacking followed by hot pressing. These composites, containing various amount of flax, failed ductilely with pronounced crack growth. Therefore, to determine their fracture mechanical behaviour the J-integral resistance curve concept (J–R) was applied. As the crack growth could not be traced, attempt was made to use the located acoustic emission (AE) events for that purpose. It was established that weighting and smoothing the located cumulative AE amplitudes the crack path can be correctly reconstructed. This was proved by collating the AE results with those derived from infrared thermographic (IT) inspection. Knowing the crack propagation at each point of the force–displacement curves the J–R curves could be determined. Both critical or initiation J-integral and tearing modulus went through a minimum with increase of flax content in the composites.     

The energy release rate and the J-integral in nonlocal micropolar field theory

The recent theory of nonlocal micropolar continuum is used to derive explicit expressions for both the energy release rate and J-integral. It was shown that this J-integral has a physical meaning of the energy release rate and, for homogeneous body with the straight crack, is path independent. It was also shown that the influence of nonlocality is contained in J-integral which allows one to discuss several special cases.     

The use of ΔK when examining microstructural effects on small fatigue crack growth

The behaviour of small fatigue cracks has been studied in the Al---Li---Cu---Mg---Zr alloy 8090. It was found that the crack inclination normal to the surface of the specimen made crack deflections and kinking in the plane of the specimen surface irrelevant to the crack driving force. The low closure levels associated with small fatigue cracks reduce the effect of microstructure on crack growth but this does not affect the ability of ΔK (stress intensity factor range) to detect microstructural influences. The use of ΔJ (J-integral range) as a correlating parameter reduced the differences between the data for long and short fatigue cracks. However, there was no evidence that ΔJ was superior at identifying microstructural effects. Similarly the effect of the higher-order terms on the value of ΔK was found to be minor. It is concluded that the use of ΔK is not likely to bias the microstructural effects and so ΔK may be used when examining microstructural effects on small fatigue crack growth.     

Mechanics of mixed mode small fatigue crack growth

An elastic-plastic analysis of a mixed mode crack was conducted under general yielding conditions using a finite element method. Based on the finite element analysis, a formula of the J-integral was developed, and the behavior of the crack opening or sliding displacement was investigated. Crack growth mechanics was discussed to explain mixed mode growth. A model expressed by the J-integral was proposed assuming that the crack growth is determined by the linear summation of relations of pure Mode I and II crack-tip deformation. The crack growth rate obtained using Inconel 718 thin-wall tubular specimens was correlated with the range of ΔJ evaluated from the proposed formula. The crack growth equations in terms of ΔJ for three different biaxial strain ratios were compared with the relations expected from the proposed crack growth model. The difference between the experimental results and the estimation was discussed from the viewpoint of crack closure and the geometry of the surface crack.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Fatigue-fracture behavior of 5083-0 aluminum-magnesium alloy for LNG applications

Low temperature mechanical properties (including fatigue) of 5083-0 Al alloy are reviewed. Based on the results in the literature, the life of notched components under fatigue loaded conditon at LNG temperature (−162°C) are predicted. Probable reasons for low fatigue crack propagation life at low temperature are discussed. A procedure to theoretically generate the strain vs life plot is indicated. An elasto-plastic model presented by El-Haddad et al. [Int. J. Fracture 16, 15–30 (1980)] is used to study the effect of low temperature on J-integral values.     

高速列车制动盘SiCp／A356颗粒增强铝基复合材料的热疲劳性能研究

通过SiCp／A356颗粒增强复合材料切口试样在20℃-300℃循环下的热疲劳试验,获得热疲劳裂纹形成寿命与试样切口半径及厚度等几何尺寸的关系。采用热弹塑性有限元法模拟热疲劳试验中试样切口根部的应力．应变响应,进而揭示出残余应力形成机制。结合热疲劳试验的裂纹形成寿命与有限元模拟的应力．应变响应,建立起考虑平均应力影响的...     

Some problems in the J-integral

For a blunt crack the j-integral is path dependent on contours which are very close to the crack tip even for elastic material. Using the incremental J-integral theory we introduce a new parameter J_t, characterizing the behavior of a crack tip and prove that the J-integral is almost path independent on contours whose radii are greater than several COD if σ_ij,1Δε_ij — ε_ijΔσ_ij = 0 in plastic regions for elasto-plastic material.     

Determination of stress intensity factors and J-integrals using the method of caustics

Applications of the optical shadow method of reflective caustics to the measurement of the stress intensity factor and J-integral in various specimens are investigated. The necessary experimental requirements to help in determining an accurate stress intensity factor and J-integral are described. The ratios of r₀ (radius of initial curve)/r_p, (plastic zone size) and r₀/t (thickness of specimen) are found to be very important experimental parameters with which to obtain meaningful stress and/or strain intensities surrounding crack tips. The appropriate ranges to determine accurate values of stress intensity factor and J-integral for polycarbonate (compact tension) and aluminum (c-shaped tension) specimens are presented.     

Evaluation of fatigue crack initiation life from a notch

Local strain at the notch-root and its effect on fatigue crack initiation was investigated in four metals by the real-time, fine-grid method. Special attention was focused on local notch-root strain behaviour until crack initiation. From the application of strain hysteresis at the notch root, the maximum strain under loading conditions during each cycle was investigated in detail. One of the main results was that the maximum strain value at the first cycle of the fatigue test coincided with that at crack initiation. Maximum strain defined from the cyclic strain changes at the notch root was proposed as one possible parameter for estimating fatigue crack initiation life. Based on the curvilinear relationship between maximum strain and number of cycles to crack initiation, a new life evaluation method for fatigue crack initiation is proposed. This approach differs fundamentally from the usual fracture mechanics method based on the stress intensity factor.     

J-integral analyses of plate and shell structures with through-wall cracks using thick shell elements

A new evaluation method using thick shell elements is proposed to calculate the distribution of the J-integral values along crack fronts of through-wall cracks in plate and shell structures. Dividing tentatively the thick shell elements into several layers in the thickness direction, integral paths are defined at each layer to obtain the thickness distributions of the J-integral values of through-wall cracks in plate and shell structures. The three-dimensional definition of the J-integral is used to calculate the J-integral value at each layer. The results of several stress intensity factor analyses are presented to show the effectiveness of the present evaluation method. The distribution of the J-integral value along a crack front is also compared between the methods using the thick shell elements and the three-dimensional solid elements.     

Fatigue crack initiation at notches in SA 333 piping steel

Abstract

In this paper are reported two recent investigations into crack initiation at notch roots using techniques developed for remote monitoring of crack growth in high–temperature water environments. In the first, a notched compact–type specimen of a carbon steel, SA 333 Gr. 6, was monitored for crack initiation (defined as a 0·076 mm crack at the notch root) in a variety of water chemistries and testing conditions. The mechanical conditions at the notch root have been analysed using the Neuber–notch method, enabling a direct comparison to be made with the strain–controlled fatigue data curves used for a smooth specimen in the ASME Boiler and Pressure Vessel Code, Section III. In the second investigation a different method was considered for monitoring crack initiation. A modification of the electrical–potential technique, called the reversing dc electrical potential method, was used to obtain quantitative information on the initiation and early growth of small surface cracks in notched bars of a high–strength alloy at elevated temperature. Results obtained by the method are presented and discussed.

MST/72     

Fatigue crack growth in double cantilever beam specimen with an adhesive layer

A test method based on fracture mechanics concepts is applied to measure fatigue crack growth rates for an adhesive material in a bondline double cantilever beam specimen containing a cohesive crack. Tension–tension tests are conducted with a stress ratio of 0.5 and at 5 Hz. Debond growth rates are measured using a compliance method. Corresponding changes in J-integral are computed based on the beam on elastic–plastic foundation analysis of the specimen. There are three bondline thicknesses that are evaluated. When computed, ΔJ are plotted against the measured debond growth rates, the results showing a power law relationship which characterizes the debond behavior for a given bondline thickness. The increase of bond line thickness has a significant effect on fatigue crack growth. The larger the bond line thickness, the larger is the fatigue crack growth resistance.     

非比例载荷下缺口件疲劳寿命预测

针对Mod.9Cr-1Mo铁素体钢缺口件进行了一系列非比例载荷低周疲劳试验,采用直流电位差法测量裂纹萌生寿命,比较了缺口半径和应变路径对疲劳裂纹萌生寿命的影响。结果表明,缺口件裂纹萌生寿命占总寿命的比例与材料类型、应变路径相关,更与缺口半径尺寸直接相关。同一路径下,随着缺口半径增加,裂纹萌生寿命所占比例增大。采用Neuber律进行缺口局部应力-应变损伤的计算,结合Smith-Watson-Topper (SWT)模型和Kandil-Brown-Miller (KBM)模型进行疲劳寿命预测。结果表明,除单轴路径和比例路径外,SWT模型得到的预测结果偏于不安全;KBM模型除对单轴预测偏于保守外,其他预测值较好,总体预测结果位于2倍分散带内。     

Adaptive finite element analysis of crack propagation in elastic fracture mechanics based on averaging techniques

A goal-oriented a posteriori error estimator is presented in this paper for the error obtained while approximately evaluating the J-integral in elastic fracture mechanics using the finite element method. The J-integral provides a criterion for crack propagation of a pre-existing crack. Its accurate evaluation is therefore of considerable importance in engineering applications to prevent failure of structures. This goal can be attained by adaptive finite element methods based on the well-established strategy of solving an auxiliary dual problem in order to control the error of a (non)linear functional, here the J-integral. In this paper, the adaptive strategy is based on a goal-oriented a posteriori error estimator that uses averaging techniques. The paper is concluded by a numerical example that illustrates our theoretical results.