Numerical study on crack propagation in functionally graded CNT-reinforced composite plates

This paper presents a numerical method for simulating the crack propagation in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The numerical method is based on 2-D natural element method (NEM) which can overcome the inherent demerits of FEM and conventional meshfree methods. The 3-D displacement field of cracked orthotropic plate is formulated using the (1, 1, 0)* hierarchical model and approximated by 2-D NEM. The thickness-wise mixed-mode stress intensity factors (SIFs) are computed using the modified interaction integral I^(1,2) and the 2-D complex-valued crack-tip singular fields. The crack propagation angle is determined by the modified maximum circumferential stress (MCS) criterion, and the crack trajectories are predicted by an incremental crack propagation simulation scheme. The present numerical method is verified from the comparison of predicted crack trajectories with the published reference solutions. Moreover, using the developed numerical method, the crack trajectory characteristics of FG-CNTRC plates are parametrically investigated with respect to the major parameters. From the parametric investigation, it is found that the crack trajectories of FG-CNTRC are significantly influenced by the material orientation angle and the stiffness ratio. But, the effects of the initial crack angle and the volume fraction and volume fraction pattern of CNTs are not remarkable.

     

基于最大能量释放率原理的裂纹扩展算法的改进

在基于最大能量释放率判据(Maximum energy release rate,MERR)的复合型裂纹扩展分析中,因需要对多个虚拟裂纹扩展方向进行试算和迭代运算,这会大大增加计算量,特别是为保证计算精度不得不选取很小的试算转角增量时,该问题会很突出。为此,提出分别基于有限差分法(Finite difference method,FDM)和最大周向应力判据(Maximum tangential stress,MTS)的裂纹转角预测方法,以减小计算量或提高计算精度。推导相关计算公式和算法,利用FORTRAN与ANSYS参数化设计语言(ANSYS parameter design language,APDL)语言混合编程的方法实现了基于ANSYS有限元环境下的裂纹扩展自动分析,并通过对带孔薄板的疲劳裂纹扩展分析,验证了所提出方法的有效性。分析发现,FDM的预测误差小于MTS的预测误差。MTS预测的转角误差曲线与转角曲线的一阶导数有相同的变化规律,而FDM预测转角的误差曲线与转角曲线的二阶导数有相同的变化规律。根据MERR和MTS判据得到的K_(Ⅱ)值趋近于零,这与局部对称判据(Local symmetry,LS)一致,但MERR和LS判据的计算结果更接近。     

A fracture mechanics life prediction methodology applied to dovetail fretting

This work evaluates a fracture mechanics based crack growth life prediction methodology for dovetail fretting fatigue laboratory experiments. The Ti–6Al–4V specimens were configured with angles of 35°, 45° and 55°. Experiments were conducted with constant amplitude loading at R of 0.1 and 0.5 with lives ranging from 100,000 to 10 million cycles. The approach included the contact loads and bulk stress calculated from the finite element method as inputs to the stress and life analysis. Contact stresses were calculated using the contact stress analysis software CAPRI. These stresses were input into a stress intensity factor calculation at the edge of contact. Crack propagation life was calculated from an assumed initial crack size. Analysis showed that propagation consumes a majority of the total life and is insensitive to a large range of initial crack sizes.     

齿轮点蚀破坏过程的力学分析

本文利用裂纹面的边界条件建立奇异积分方程,通过解奇异积分方程求得裂纹尖端的应力强度因子,并运用裂纹扩展理论对疲劳裂纹的扩展方向进行了分析。结果表明齿面垂直裂纹将沿与齿面约20°角且与齿面摩擦力相反的方向扩展,而分叉裂纹将沿与斜裂纹段约60°的方向向齿面扩展。     

Surface and Subsurface Cracks in Rolling Contact Fatigue of Hardened Components

The competitive aspect of surface and subsurface fatigue crack propagation in hardened components subjected to rolling contact fatigue is highlighted, the former being greatly affected by the working conditions (in particular the presence of tangential stresses and lubricant), the latter depending mainly on the inclusions content and on the hardness profile. In order to determine which one of these kinds of damage is favoured, initial data consisting of contact load, rolling and sliding speed, theological properties of the lubricant, material hardness and inclusions content are necessary.

The concurrent role of asperities and Hertzian stress field in determining surface crack propagation is explained with the approach of the “quiescent zone.” calculating the stress intensity factors range in a contact cycle and considering the pumping effect of the fluid possibly present on the contact surface.

Inherent defects (especially oxides) are thought to be responsible for subsurface cracks origin and the Murakami formula for short cracks is extrapolated to describe their growth threshold, which also depends on the hardness and therefore on the depth in surface hardened components.

A crack propagation index is then defined as a ratio of applied to threshold stress intensity factor, both for surface and subsurface cracks. Evaluating this index for a general operating condition, it is possible to determine which damage mechanism is favoured, taking into account the decisive effect of the hardness profile.     

Dynamic crack growth in TDCB specimens

Dynamic crack propagation in tapered double cantilever beam (TDCB) specimens is analysed via beam theory and the finite element method. Steady state and transient solutions of the energy release rate G are given for various load conditions. Finite element analysis is performed to obtain the dynamic G at given crack speed or the crack history for a given fracture toughness. The stress wave effects on the dynamic G are discussed. The beam solutions are compared with the finite element results and some experimental phenomena are explained.     

Fatigue crack propagation behavior in STS304 under mixed-mode loading

The use of fracture mechanics has traditionally concentrated on crack growth under an opening mechanism. However, many service failures occur from cracks subjected to mixed-mode loading. Hence, it is necessary to evaluate the fatigue behavior under mixed-mode loading. Under mixed-mode loading, not only the fatigue crack propagation rate is of importance, but also the crack propagation direction. In modified range 0.3≤a/W≤0.5, the stress intensity factors (SIFs) of mode I and mode II for the compact tension shear (CTS) specimen were calculated by using elastic finite element analysis. The propagation behavior of the fatigue cracks of cold rolled stainless steels (STS304) under mixed-mode conditions was evaluated by using K_I and K_II(SIFs of mode I and mode II). The maximum tangential stress (MTS) criterion and stress intensity factor were applied to predict the crack propagation direction and the propagation behavior of fatigue cracks.     

Two approaches to taking nonsingular <Emphasis Type="Italic">T</Emphasis>-stresses into account in the criteria of fracture mechanics for bodies with notches

Two possible models and criterion equations of fracture mechanics for bodies with notches taking into account nonsingular expansion terms of stresses at the notch (crack) apex based on crack-growth resistance diagrams and a master curve are considered. A criterion equation of a generalized crack-growth resistance diagram admissible for a body with a crack and a notch and taking into account the changes in the degree of strain constraint at the notch apex due to finiteness of its apex radius rounding and a nonsingular stress component (T-stresses) is given. The notion of effective T-stresses determined using averaging of T-stresses in front of the notch apex in the pre-fracture zone characterized by effective scattering in introduced. A basic dependence of fracturing viscosity in the function of effective T-stresses (a master curve) of pipe steel is constructed for the given notch geometry.     

Influences of equal biaxial tensile loads on the stress fields near the mixed mode crack

A hybrid method for photoelasticity is introduced and applied to the plane problems of isotropic polycarbonate plates with a central crack under uniaxial and equal biaxial tensile loads. Also, the influences of equal biaxial tensile loads on the isochromatic fringes, stress fields and stress intensity factors near the mixed mode crack-tip have been investigated. The results show that, when an equal lateral tensile load is added to the specimen under uniaxial tensile load, the asymmetric isochromatic fringes about the line of crack gradually become symmetric, and the slope of the isochromatic fringe loop near the crack-tip is inclined towards the crack surface according to the increasing of the inclined angle of crack. Furthermore, the shapes of distribution of all stress components are changed from asymmetric to symmetric. In the equal biaxial tensile load condition against the uniaxial tensile load condition, the values of stress intensity factors are changed little, and only the region of compressive stress of σ _x /σ _O is changed when β = 0°, but the values of K _I /K ₀ are increased and those of K _II /K ₀ become almost zero, namely, we have the mode I condition when β = 15°∼45°. This paper was recommended for publication in revised form by Associate Editor Chongdu Cho Dong-Chul Shin received the B.S., M.S. and Ph.D. degrees in Mechanical Engineering from Yeungnam University in 1995, 1997 and 2001, respectively. Dr. Shin studied at the University of Tokyo, Japan, for three years (from April, 2005 to January, 2008) as a Post-Doctoral fellow (supported by Korea Research Foundation (KRF) and Japan Society for the Promotion of Science (JSPS)). Dr. Shin is currently a Research Professor at the School of Mechanical Engineering at Pusan National University, Korea. His research interests include the static and dynamic fracture mechanics, stress analysis, and fracture criteria of piezoelectric ceramics, etc. Jai-Sug Hawong received a B.S. in Mechanical Engineering from Yeungnam University in 1974. Then he received his M.S. and Ph.D. degrees from Yeungnam University in Korea in 1976 and from Kanto Gakuin University in Japan in 1990, respectively. Prof. Hawong is currently a professor at the School of Mechanical Engineering at Yeungnam University, in Gyeongsan city, Korea. He is currently serving as vise-president of Korea Society Mechanical Engineering. His research interests are in the areas of static and dynamic fracture mechanics, stress analysis, experimental mechanics for stress analysis and composite material etc.     

The Griffith-Orowan fracture theory revisited: The T-Criterion

In the present paper a new fracture criterion (the T-criterion) is described. It is based on the Griffith fracture theory, as modified by Orowan, according to which failure is the result of the mutual action of both fracture and yielding mechanisms. The main idea of the T-criterion is that fracture is caused by normal stresses, whose contribution is included in the dilatational part T_V of the strain-energy density. It is then postulated that fracture will initiate outside the plastic region surrounding the crack-tip, when T_V reaches a critical value. On the other hand, plasticity depends on the distortional part of strain-energy density and its extent is defined by the Mises yield locus, which is used for the calculation of the elastic-plastic boundary, along which T_V is computed. Then, the T_V = f() curve around the crack constitutes a physically sound curve of the distribution of the total elastic strain-energy density there.Then, the critical T_V,0- and T_D,0-parameters control the failure behaviour of the material and, thus, the T-criterion can distinguish between failure by fracture or yielding. A study is made on the relative validity of the expected angle of crack propagation, especially in ductile materials. Different predictions are obtained from the T-criterion, as they are compared to those of an up-to-now popular criterion suitable only for brittle fractures. Experimental data show good agreement with the predictions of the T-criterion, especially for the critical stress for fracture.     

Constitutive Model for an FCC Single-Crystal Material

Taking into account the effects that the components of tension stresses couple with components of torsion stresses when off-axis loads are applied to orthotropic materials, Hill’s yield criterion for plastically orthotropic solids is modified by adding an invariant that is composed of the product item of quadratic components of the deviatoric stress tensor, and a new yield criterion is put forward in terms of the characteristics of the face-centered cubic (FCC) single-crystal material. The correlation of prediction and experiments is very good, and the new criterion is used to predict the yield stresses of an internal single-crystal, Nickel-based superalloy, DD3, which is more accurate than that of Hill’s at 760°C. Equivalent stress and strain that adapt to the new criterion are defined. Thinking of the yield function as a plastic potential function from the associated flow rule, the elastic-plastic constitutive model for the FCC single-crystal material is constructed, and the corresponding elastic-plastic matrix is educed. The new yield criterion and its equivalent stress and strain will be reduced to Von Mises’ yield criterion and corresponding equivalent stress and strain for isotropic materials. Translated from J. Cent. South Univ. (Sci. Technol.), 2004, 35(3) (in Chinese)     

2-D discontinuous chip cutting model by using strain energy density theory and elastic-plastic finite element method

The formation of discontinuous chip is investigated in this paper. The cutting simulation was conducted on 60–40 brass (60% Cu, 40% Zn) under an extremely low cutting speed. The region of the maximum strain energy density (SED) distribution value relative to the minimum value, i.e. (dw/dv)_min^max, was used as the criterion to predict the initial breakage location under the presumption that the curvature direction of the maximum SED was the direction of crack growth. The shape and cutting force of discontinuous chip crack, the stress and strain distribution of the workpiece and chip, and the variation of various nodal force on the chip–tool interface were derived.     

Fatigue cracks at notches

The failure of a component or specimen due to a fatigue crack growing from a notch is considered. Previous methods of analysis involving stress and strain concentration factors are shown to be inadequate. By defining equivalent cracks in notched and un-notched situations as cracks with equal growth rates, the concept of notch contribution to crack length is introduced. Theoretical notch contributions are obtained for a variety of central and edge elliptical notches via stress intensity factor solutions. These results when extended to a very wide range of general notch shapes can be reduced to a useful and simple design rule where e is the contribution to a crack of length l growing from a notch of depth D and root radius . This rule combines the size and shape effects long known to affect fatigue behaviour and defines the extent of the notch field as 0·13√(D).The fatigue crack propagation lives of a wide variety of notches were estimated by this rule and comparisons with experimental values revealed very small errors normally well within the scatter of fatigue lives.The design rule is extended to enable the conventional stress intensity factor method to be employed. A fatigue concentration factor is proposed which takes into account the presence of a fatigue crack which all previous methods have ignored.     

分形裂纹扩展对材料疲劳行为的影响

研究了分形裂纹扩展对材料疲劳行为的影响。在实验观测的基础上建立了分形裂纹扩展模型。研究表明，分形裂纹扩展分维Ｄ是裂纹弯折角θ的函数，分形裂纹扩展在裂纹尖端由于弯折而形成“局部混合模式”和裂纹的分形长度效应均很强地影响疲劳裂纹的有效应务强度与有效裂纹扩展速率。本文的理论民一些材料的实验结果取得了很好的一致。     

Crack Propagation of Rolling Contact Fatigue in Ball Bearing Steel Due to Tensile Strain

Crack propagations or failure modes in rolling element bearings, which had been difficult to explain via conventional crack propagation mechanisms such as the orthogonal shear stress mechanism, were discussed from the viewpoint of a tensile strain mechanism. Contact stresses are compressive in three axes, whose values differ from each other; then strain can be tensile in one of these directions, acting at a right angle to the direction of maximum compressive stress. A crack is considered to propagate by this tensile strain. When contact stress is small, a crack produced by some cause can propagate by this elastic tensile strain. When contact stress is large, residual tensile strain is produced by plastic deformation, which can also influence the crack propagation. Several failure modes of rolling element bearings, which had been difficult to explain, were explained by tensile strain.     

In-process estimation of fracture surface morphology during wheel scribing of a glass sheet by high-speed photoelastic observation

Defect-free glass separation techniques are in strong demand in glass processing industries. In this study, we intended to observe the internal stress field during/after wheel scribing of a glass sheet using the photoelastic method. First, we visualized the crack propagation behavior in a 0.7-mm-thick non-alkali glass sheet during mechanical scribing with a 2.0-mm-diameter serrated diamond wheel using high-speed imaging techniques. The observation results under various applied load conditions showed that the crack propagation behavior changed dramatically at a load of approximately 9–10 N; the generated crack hardly propagated in the thickness direction under lower load conditions, in contrast to the rapid propagation under higher load conditions. The fracture surface morphology that was observed after cleavage also changed, from damaged to defect-free surfaces with increments in the applied load around the transition point (9–10 N). This result indicated that the fracture surface morphology was determined by the crack propagation behavior. Second, the birefringence phase difference was measured from the upper side of the glass sheet to enable understanding of the stress fields induced by scribing wheel indentations. As a result, the phase differences that were distributed along the scribe line were shown to differ depending on the applied loads; the phase difference changed little under lower load conditions, but vanished immediately under higher load conditions. Therefore, these differences were dependent on whether or not rapid crack propagation occurred. The measured phase difference distribution thus included information about the crack propagation behavior, and this information could be used as a criterion for estimation of the fracture surface morphology. An in-process estimation method for the fracture surface morphology during mechanical wheel scribing was therefore developed based on high-speed polarization imaging techniques.     

A study of spur gear pitting formation and life prediction

In this study, a numerical prediction on pitting formation is carried out in spur gear made from austempered ductile iron. General two-dimensional rolling sliding contact situations are considered for the development of the analytical model. The problem is assumed under linear elastic fracture mechanics and the finite element method is used for numerical solutions. Mixed mode stress intensity factors K_I and K_II for cyclic loading are evaluated and related to crack extension by a Paris-type equation. The maximum tangential stress criterion is used to determine the crack-turn-angle during crack propagation under cyclic loading.A series of experimental study is also carried out to determine the pitting formation life. Test specimens were first austenitized in salt bath at 900 °C for 90 min after which they were quenched in salt bath at 325 and 425 °C, for 60 min. A comparison is carried out between numerical and experimental results.     

30Cr2Ni4MoV转子钢II型裂纹的疲劳扩展行为

材料疲劳裂纹扩展(Fatigue crack propagation,FCP)速率是表征材料抗疲劳破坏的重要力学性能指标,是对核反应堆工程、化工、航空、航天、高铁等关键工程进行结构完整性评价的重要依据。采用Arcan试样对30Cr2Ni4MoV转子钢的II型裂纹疲劳扩展行为进行研究,结合已有裂纹扩展方向预测准则对II型裂纹疲劳扩展方向进行预测,结果表明,最大周向应力准则可以较好地预测II型裂纹疲劳扩展方向。采用紧凑拉伸(Compact tension,CT)试样获取30Cr2Ni4MoV转子钢的I型裂纹疲劳扩展速率,对比I型裂纹和II型裂纹的疲劳扩展试验获得的FCP速率与J积分范围关系趋势,二者较为接近。针对30Cr2Ni4MoV转子钢,依据Arcan试样获得的II型裂纹疲劳扩展速率试验结果可用于结构裂纹扩展剩余寿命的预测。