Dugdale model for strain hardening materials

A Dugdale model for hardening materials under plane stress conditions is proposed. Crack tip opening displacements (CTODs) of different geometries, compact, center crack tension, double edge crack tension and three point bend specimens, have been calculated by means of the weight function method. The results have been compared with the J-integral from EPRI's handbook [Y. Kumar, M.D. German and C.F. Shih, EPRI NP-1931, Project 1237-1, Technical Report (1981)] for strain hardening exponent n = 3, 5,7,10,13,16,20 and two different Ramberg-Osgood coefficients. The results indicate that the proposed model could well correlate CTODs from the Dugdale model and the J-integral, thus it is an alternative tool to take account of the strain hardening effect in engineering applications.     

On the validity of the Dugdale model for craze zones at crack tips in PMMA

Journal of Materials Science -     

Two cracks with coalesced interior plastic zones — The generalised Dugdale model approach

The problem investigated is of an elastic-perfectly plastic infinite plate containing two equal collinear and symmetrically situated straight cracks. The plate is subjected to loads at infinity inducing mode I type deformations at the rims of the cracks. Consequently, plastic zones are formed ahead of the tips of the cracks. The loads at infinity are increased to a limit such that the plastic zones formed at the neighbouring interior tips of the cracks get coalesced. The plastic zones developed at the tips of the cracks are closed by applying normal cohesive quadratically varying stress distribution over their rims. The opening of the cracks is consequently arrested. Complex variable technique is used in conjugation with Dugdale’s hypothesis to obtain analytical solutions. Closed form analytical expressions are derived for calculating plastic zone size and crack opening displacement. An illustrative numerical example is discussed to study the qualitative behaviour of the loads required to arrest the cracks from opening with respect to parameters viz. crack length, plastic zone length and inter-crack distance. Crack opening displacement at the tip of the crack is also studied against these parameters.     

A model of fatigue crack growth based on Dugdale model and damage accumulation

The modified Dugdale model given by Budiansky-Hutchinson and a Coffin-Manson type damage law are used to calculate the cumulative fatigue damage of material elements at the tip of a fatigue crack. From this analysis a fatigue crack growth equation is obtained which gives predicted crack growth rates in reasonable agreement with experimental data for two aluminium alloys 7075-T6 and 2024-T81, two titanium alloys Ti-8A1-1Mo-1V and Ti-6A1-6V and a PH13-8Mo stainless steel. Limitations of this new fatigue crack growth model are also discussed.     

Dugdale yielded zones in cracked sheets of glassy polymers

Photoelastic measurements on centrally notched sheets of polycarbonate have been used to confirm the elastic stress field around the yielded zone predicted by the Dugdale model. By comparing the behaviour of polycarbonate, polysulfone and Polyvinylchloride the plasticity requirements of the model have been investigated. The residual elastic stress fields in unloaded specimens have been interpreted in terms of a lower compressive than tensile yield stress.     

A comment on ″On the validity of the Dugdale model for craze zones at crack tips in PMMA″

Journal of Materials Science -     

On a mixed-mode Dugdale model

Summary A model attributed to Dugdale provides a correction for plasticity effects at crack tips in Mode I, under the assumption of small-scale yielding. Similar models have been proposed for Modes II and III, the former fairly recently. In the present study, the Dugdale model is extended to cases combining Modes I, II and III, based on the von Mises yield criterion. The combined model provides an a posteriori estimate for plasticity effects, based only on the stress intensity factors from the elasticity solution. It also provides an estimate for the crack-opening displacement and theJ-integral value. In the limit of small loads, the corresponding elastic results are recovered.     

Closed-form factors for an edged-cracked cylindrical bar Dugdale model

Closed-form equations are given for the plastic zone size and crack tip opening-displacement in a circumferentially-cracked cylindrical bar under tension, treated in terms of a Dugdale-type model. The equations are valid from a lower limit of linear-elastic behaviour up to the intervention of a limit-load failure mechanism. They have been derived by fitting a previously given set of semi-empirical equations to finite-element data for this geometry, derived from the literature.     

Weight function based Dugdale model for mixed-mode crack problems with arbitrary crack surface tractions

Weight function theory states crack surface displacements can be found for any arbitrary distribution of mode I, or mixed-mode crack face tractions via that geometry’s weight functions. This statement is validated via finite element analysis of the infinite center-cracked plate for various mixed mode loadings. An elastic-perfectly plastic material is considered using a Dugdale approach and compared to elastic-plastic finite element simulations. The weight function method in all cases agrees well with the finite element simulations for small scale yielding at the crack tip. As the maximum traction value approaches one-half the yield strength discrepancies become larger due to violation of small scale yielding.     

Dugdale model solutions for a single edge cracked plate

International Journal of Fracture - A technique for improving the convergence rate of the Gauss-Seidel iterative procedure for finite element analysis is discussed. It is noted that this technique...     

Crack arrest model for a piezoelectric plate — A generalised Dugdale model

The constant search for new materials has provided impetus to research in piezoelectric materials. An anti-plane problem for a cracked unbounded two-dimensional poled piezoelectric plate has been investigated. The crack rims open on account of shear mechanical forces applied at the remote boundary and in-plane electric displacement field prescribed at the infinite boundary. Thus the crack yields both mechanically and electrically. Consequently, a plastic zone and a saturation zone protrude ahead of each tip of the crack. These developed zones are in turn closed by applying yield point shear stress at the rims of plastic zone and normal closing saturation limit displacement on the rims of saturation zones. Two cases are investigated when (i) the developed saturation zone length exceeds that of the developed plastic zone, and (ii) saturation zone length is smaller than that of the plastic zone. Fourier integral transform method is used in each case to obtain the length of plastic zone and saturation zone. Closed form analytic expressions are obtained in each case. Crack opening displacement and potential drop across the rims of the crack are also obtained. The effect of mechanical loads on crack closure in the presence of electric field is investigated and vice-versa. Also energy release rate expressions are obtained for both the cases.     

Dugdale model for circumferential through-cracks in pipes loaded by bending

The paper contains an analytical solution to the title problem by means of the semi-membrane theory of cylindrical shells. Results include the crack opening displacements as a function of circumferential angle, the fracture parameter J, and the effects of the crack on the compliance of the pipe.

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Résumé L'étude comporte une solution analytique du modèle de Dugdale appliqué au cas envisagé, en recourant á la théorie des semi-membranes dans les enveloppes cylindriques. Les résultats donnent la relation entre les déplacements d'ouverture de la fissure et l'angle circonférentiel, le paramètre de rupture J, ainsi que les effects de la fissure sur la compliance du tube.

     

A strain-based Dugdale model for cracks under generally yielding conditions

To develop an analytical method for quantifying the growth behaviour of short cracks embedded in notch plastic zones, a critical assessment of the Dugdale model is first made by comparison against finite element analysis for an edge-cracked plate subjected to an applied strain varying linearly along the crack path. It is shown that the conventional stress-based Dugdale model provides accurate estimates for the crack-tip opening displacement and the plastic zone size provided that the applied strain does not exceed one third of the yield strain. These estimates become significantly inaccurate at higher strain levels. To overcome this limitation of the conventional model, a strain-based implementation of the Dugdale model is proposed in which the conventional equilibrium equation is replaced by strain compatibility. Comparison with finite element results shows that this strain-based model provides accurate values for both the crack-tip-opening displacement and the plastic zone size for applied strains up to four times the yield strain and with no evidence of decreasing accuracy with increasing strain. Furthermore, it is shown that the relevant plastic constraint factor to be used for plane strain is that appropriate for the notch plastic zone in the absence of a crack, rather than the more usual choice which is appropriate only for small-scale yielding conditions. This provides a practical and physically plausible approach for extending the scope of current predictive software for fatigue crack growth based on the Dugdale model to include conditions of large-scale yielding.     

Moving Dugdale crack along the interface of two dissimilar magnetoelectroelastic materials

In this paper, the concept of Dugdale crack model and Yoffe model is extended to propose a moving Dugdale interfacial crack model, and the interfacial crack between dissimilar magnetoelectroelastic materials under anti-plane shear and in-plane electric and magnetic loadings is investigated considering the magneto-electro-mechanical nonlinearity. It is assumed that the constant moving crack is magneto-electrically permeable and the length of the crack keeps constant. Fourier transform is applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. The explicit expression of the size of the yield zone is derived, and the crack sliding displacement (CSD) is explicitly expressed. The result shows that the stress, electric and magnetic fields in the cracked magnetoelectroelastic material are no longer singular and the CSD is dependent on the loading, material properties and crack moving velocity. The current model can be reduced to the static interfacial crack case when the crack moving velocity is zero.     

Validity limits of the Dugdale model for thin cracked plates under biaxial loading

Experimental results show that there are significant biaxial effects on the fracture behaviour of thin cracked plates. In this paper we examine the possibility of extending the Dugdale model in the presence of biaxial loads. This investigation is mainly concerned with the validity limits of the model in respect of the plastic flow rules. Through a careful analysis of the correspondence between applied and local stresses, it is shown that the Dugdale model fails when the applied stress parallel to the crack plane is higher than the applied stress normal to it. In this case the flow rules are significantly violated.     

Nonlinear damage creep model based on fractional theory for rock materials

Mechanics of Time-Dependent Materials - In this study, based on the first application of Caputo fractional derivative with respect to the Mittag–Leffler and power functions, two improved...     

A practical method for determining Dugdale model solutions for cracked bodies of arbitrary shape

A method is proposed to determine Dugdale model solutions for cracked bodies of arbitrary shape. The method is based on the determination of stress intensity factors for component loading systems and superposing these such that singular behaviour is eliminated. The desired crack opening displacement is then determined trivially. Results are presented for five cases of practical interest and the method is directly applicable to problems of a general nature.     

Damage constitutive relations for composite materials

This work is devoted to the study of damage, especially in composite materials. For these media, a kind of damage comes from a possibility of debonding between fibers and matrix, involving the appearing of microdefects as microvoids or microcracks. In these situations, our purpose is to prove that using jointly the homogenization method and thermodynamic theory of generalized standard materials, we can get damage evolution laws to describe the macroscopic behavior of composite media.     

基于模型修正的钢管焊接结构焊缝损伤识别

摘要：本文提出了一种基于模型修正的钢管焊接结构焊缝损伤识别方法。利用从发射台骨架试验模型获取的模态参数,选择识别结果中精度较好的模态频率作为模型修正的基准频率。通过对待修正参数的灵敏度分析,运用ANSYS和MATLAB软件对有限元模型进行了修正。以实测模态和计算模态之间的误差建立一个带约束边界非线性最小二乘目标函数,将损伤识别问题转化为优化问题,并采用信赖域方法求解该优化问题。以有限元模型焊接结点单元组弹性模量的降低模拟焊缝损伤,并假定了两种损伤工况,通过对发射台骨架模型的数值仿真及试验研究,结果表明本文提出的损伤识别方法识别效果较为理想,为解决这种复杂焊接结构焊缝损伤识别问题提供了新的思路。