Sandia Fracture Challenge: blind prediction and full calibration to enhance fracture predictability

The Impact and Crashworthiness Lab at Massachusetts Institute of Technology participated in the Sandia Fracture Challenge and predicted the crack initiation and propagation path during a tensile test of a compact tension specimen with three holes (B, C, and D), using a very limited number of material properties, including uniaxial tensile tests of a dog-bone specimen. The maximum shear stress and modified Mohr–Coulomb fracture models were used. The predicted crack path of A–C–E coincided with two out of thirteen experiments performed by Sandia National Laboratories, and the maximum load, as well as the load level at the first and second crack initiation, was accurately captured. However, the crack-tip opening displacements (CODs) corresponding to the initiation of the two cracks were overestimated by 12 and 24 %, respectively. After the challenge ended, we received the leftover material from Sandia and did full plasticity and fracture calibration by conducting extra fracture tests, including tensile tests, on a specimen with two symmetric round notches, a specimen with a central hole, and a butterfly specimen with double curvature. In addition, pure shear tests were carried out on a butterfly specimen. Newly identified fracture parameters again predicted the A–C–E crack path, but the force–COD response could be reproduced almost perfectly. Detailed calibration procedures and validation are discussed. Furthermore, in order to investigate the influence of the machining quality on the results, a pre-damage value was introduced to the first layer of finite elements around the starter notch, A, and the three holes, B, C, and D. This accelerated shear localization between holes A and D (and between D and C as well) and changed the crack path to A–D–C–E. Parametric study on the pre-damage value showed that there exist two competing crack paths, and the corresponding force–COD curve is influenced by the pre-damage value. The effect of mesh size and boundary conditions are also discussed.     

Micro-mechanical modelling of ductile damage and tearing – results of a European numerical round robin

ABSTRACT Results of a European numerical round robin on the application of constitutive equations for ductile damage to simulate tearing of a ferritic steel are presented. The analysis of deformation and failure of a standard smooth tensile specimen is used to characterize the material and identify critical damage parameters for ductile tearing. Ductile crack growth in a C(T) specimen is then numerically simulated by applying the constitutive models of G urson or Rousselier in order to predict a J _R -curve. Although the tensile tests were satisfactorily described, two main problems arose. The first one is that the participants' results differ considerably from each other with respect to the critical damage parameter obtained in the first task and the predicted J _R -curves in the second. The reasons were partially found in the strategies for parameter identification and the non-unique definitions for crack initiation and crack growth used in the simulations. Further reasons are expected in the individual realization of the damage model in the FE programmes or user subroutines. The second problem is a general discrepancy between the simulations and the experiment: most of the predicted J _R -curves are too flat compared with the experimental one. Manifold conclusions can be drawn for future work aiming at improving the reliability of the numerical models and promoting their application in engineering practice.     

Prediction of the Sandia Fracture Challenge using a shear modified porous plasticity model

Blind analyses of the localization and ductile fracture behavior of an arbitrarily shaped coupon, performed for the Sandia Fracture Challenge, are presented. These analyses were performed using a shear-modified Gurson porous plasticity model that was calibrated using standard mechanical test data. The blind predictions were found to be in good agreement with experimental data, thus increasing confidence in the calibration methodology where test data is not available. In addition to the analyses submitted to the Challenge, additional non-blind analyses examining the role of both as-machined versus nominal coupon geometry and the selected value of initial porosity were conducted. It was found that by capturing the as-machined, out of tolerance, geometry in numerical calculations the fracture mode was altered from tension to shear. This agrees well with the experimental observation that all in-tolerance coupons failed in a tensile mode while all out-of-tolerance coupons failed in a shear mode. Additionally, it was found that by modifying the initial void volume fraction to a lower value still within the range that the calibration methodology provided, calculations capturing this as-machined geometry were able to closely match experimental results.     

The re-characterisation of complex defects: Part I: Fatigue and ductile tearing

Defect assessment codes idealise complex defects as simple shapes which are amenable to analysis in a process known as re-characterisation. The present work examines the re-characterisation of complex defects which extend by fatigue, ductile tearing or cleavage. A family of representative defects were analysed numerically, while a related experimental programme investigated defect interaction and failure. Part I of the paper focuses on fatigue and ductile tearing. Part II examines cleavage. The numerical and experimental results are discussed within the context of the re-characterisation procedures described in BS 7910 (Guidance on methods for assessing the acceptability of flaws in metallic structures. London, UK: British Standard Institution; 1999 [Chapter 7]) and R6/4 (Assessment of the integrity of structures containing defects. Gloucester: British Energy Generation Ltd.; 2001 [Revision 4, Chapters I and II.3]).The level of conservatism of the re-characterisation procedures for fatigue and ductile tearing are discussed. A possible non-conservatism of the re-characterisation for cleavage is discussed in Part II, within the framework of constraint based statistical fracture mechanics.     

The essential work of fracture for tearing of ductile metals

A simple energy balance analysis is presented for the tearing of ductile sheet metals using the trousers test. It is shown that the specific essential work of fracture (w _e ) for tearing can be estimated by extrapolating the straight line relationship between the tearing force per unit thickness and the trousers leg width to zero leg width. There are two contributions to the specific essential work of fracture: one is due to the localised plastic shearing work in a zone contiguous with the torn edges (w _e1 ) and the other is the final out-of-plane tearing work (w _e2 ).

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Résumé En utilisant le Trousers Test, on présente une analyse simple d'équilibre énergétique dans le cas du déchirement de feuilles métalliques ductiles. On montre qu'il est possible d'estimer le travail spécifique de rupture en déchirement w _e en extrapolant la relation linéaire qui lie la force de déchirement par unité d'épaisseur et la largeur de l'échantillon caractéristique entre une valeur 0 et une valeur donnée. Deux éléments contribuent au travail spécifique essentiel de rupture, l'un est dû au travail de cisaillement plastique local dans une zone contigue aux bords de l'arrachement (w _e1 ) et l'autre est le travail de déchirement final hors du plan de la feuille (w _e2 ).

     

Some observations on the tearing of ductile materials

A relationship between tearing force and tensile properties is deduced by analogy with notched tensile failure and proves to be quite accurate in predicting the tearing forces of a wide range of materials. It is found that the elasticity modulus is a significant factor in the relationship and its role is investigated. A model of the tearing process is presented which seems to be a more accurate representation of the physical situation for many materials than those previously suggested. A simple analysis of the model leads to the relationship which is found to be experimentally reliable.     

Ductile tearing in part-through cracks: experiments and cell-model predictions

This study describes an application of the computational cell model to predict ductile crack growth measured in experiments performed on surface-cracked, thick plates fabricated from a ferritic pressure vessel steel. The cell model limits void growth and coalescence to within a thin layer of material over the crack plane. Outside this layer, the material deforms plastically but remains void free. The Gurson–Tvergaard dilatant plasticity model describes the evolution of void growth and the associated macroscopic softening within the cells. Material-specific, cell parameters readily separate into two categories: those describing the micromechanics of void growth rate and those describing the local fracture process of the cell. Calibration of these parameters utilizes both discrete (3-D) cell models and R-curves measured using standard deep-notch bend or compact tension specimens. The cell model is applied here to surface-cracked plates subjected to different loading histories of tension and bending. The calibrated cell model reproduces accurately full details of the load-deformation records and the crack growth profiles for all the cases. These numerical studies suggest that the computational approach based on the cell model provides an engineering tool to predict ductile crack growth behavior in flawed structural components.     

J-resistance curve and ductile tearing of a mild steel

The onset of ductile tearing at room temperature of mild steel BS 15 was studied using side grooved compact tension specimens. The approach to this problem was divided conveniently into two basic parts: first, identification and evaluation of the toughness at initiation of crack extension, and second, assessment and characterization of the subsequent crack growth behaviour. The critical value of the J integral for crack initiation, J_c was obtained using two different techniques: the multispecimen method and a single specimen compliance test. It was found that the latter could be used with much larger unloading than originally proposed. This has the advantage of greater accuracy in the determination of the compliance, and consequently in the evaluation of crack extension. In the second part of the work, resistance curves were obtained applying two different approaches. The resistance curves obtained following the more exact method were used for the determination of the tearing modulus T of the material, and the values thus derived, compared with a selection of other steels.     

Engineering assessment of ductile tearing in uniaxial and biaxial tension

To decide between clearly different approaches for engineering assessment of plane stress tearing, we performed uniaxial and biaxial tensile tests on middle-cracked specimens at various in-plane constraint states. Attention was focused on determination of the crack tip opening spacing δ_n, crack tip opening angle ψ_c, crack mouth opening angle α_s, energy dissipation rate R, and specific work of fracture A_s. Our experimental results demonstrate that the values of δ_n, ψ_c, α_s, R, and A_s for a high-strength low-hardening aluminium alloy all depend on the specimen geometry, its size, and the load biaxiality ratio. However, assessment of ductile tearing by interconnected characteristic quantities α_s and A_s is more preferable over the use of δ_n, ψ_c, and R values for a number of basically important reasons discussed in this paper.     

Analysis of ductile tearing using a local approach to fracture

In this paper, the Rice and Tracey (RT) model based on growth of cavities is verified in order to describe the ductile tearing in stainless steel 12Ni6Cr and aluminium alloy. Experimentally, central crack panel and compact tension specimens were tested. The comparison of the experimental results with the classical RT model shows that this model cannot make a good prediction using J −Δ a curve. On the basis of fitting procedure and numerical simulations, we have proposed a modification of this model by introducing corrective coefficients to improve the classical RT model. The proposed model, although very simple, is able to approximate with good accuracy the experimental results and that the approximation is, as expected, better than using the RT approach directly.