Dynamic crack initiation in 3PB ductile steel specimens

Conclusions The design of the experimental set-up has exposed several advantages but also one drawback: the U-shaped hammer with fixed impact heads gives uncertain boundary conditions at the impact points and thus an uncertain stress-strain state at the crack tip. The set-up will therefore be redesigned in order to avoid this uncertainty.The advantage with the U-shaped hammer is that the crack growth area of the specimen will only get a minor translation and therefore close up photography is possible. The high speed photos have shown to be an excellent way to evaluate the experiments. The CMOD can be measured with an accuracy within about 0.1 mm. Necking (which follows after crack growth in the interior of the specimen) and visible crack growth can be fairly well determined from the photos.The evaluation of the experiments is made from a combination of measurements and calculations. Excessive nonlinear dynamic FEM calculations is a necessary part of the investigation.The results indicate that the J-integral for onset of crack growth is about the same for the two lower impact velocities 15 m/sec and 30 m/sec and it is decreased when the impact velocity is increased to 45 m/sec.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 28, No. 1, pp. 69–73, January–February, 1992.     

Measurement of fracture initiation toughness and crack resistance in instrumented Charpy impact testing

A new method has been developed involving direct measurement of the load-line displacement during instrumented Charpy testing. The method uses a laser interferometer to measure displacement in addition to the load-line displacement derived from the load signal. Tests were conducted using fatigue precracked and V-notched test pieces in the temperature range +23°C to −80°C on a conventional ship grade steel, a pressure vessel steel and two welded joints. Good correlation was found between the J_0.2 initiation fracture toughness determined by the multi-specimen method and the J_i fracture toughness determined from single specimens using the new method to detect ductile fracture initiation.     

A damage model for ductile crack initiation and propagation

Damage-induced ductile crack initiation and propagation is modeled using a constitutive law with asymmetrical contraction of the yield surface and tip remeshing combined with a nonlocal strain technique. In practice, this means that the void fraction depends on a nonlocal strain. Finite strain plasticity is used with smoothing of the complementarity condition. The prototype constitutive laws take into account pressure sensitivity and the Lode angle effect in the fracture strain. Two plane idealizations are tested: plane stress and plane strain. Thickness variation in the former is included by imposing a null out-of-plane normal stress component. In plane strain, pressure unknowns and bubble enrichment are adopted to avoid locking and ensure stability of the equilibrium equations. This approach allows the representation of some 3D effects, such as necking. The nonlocal approach is applied to the strains so that the void fraction value evolves up to one and this is verified numerically. Three verification examples are proposed and one validation example is shown, illustrating the excellent results of the proposed method. One of the verification examples includes both crack propagation in the continuum and rigid particle decohesion based on the same model.     

Crack initiation condition in the specimens of ductile materials

In this paper, the elasto-plastic Finite Element Method was used to simulate the ductile fracture initiation of four kinds of specimens made of low-carbon steel No. 20 (Chinese steel), and the damage parameter V_D was calculated for these specimens. The results showed that the damage mechanics criterion V_D proposed by the author and B. X. Yang [Engng Fracture Mech. 27, 371–386 (1987)], could be applied to predict the crack initiation. Also, the relationship between the damage parameter V_Dc and the crack tip opening displacement was discussed in this study.     

Effects of microvoids on crack blunting and initiation in ductile materials

Effects of microvoid nucleation and growth on the stress and strain fields near a crack tip are studied by employing the Gurson's constitutive model of porous plastic solids and by using a finite element method suitably formulated to admit large geometry change. It is shown that microvoids nucleate and grow rapidly in the region at a distance less than the blunted tip diameter away from the crack tip and have a great influence on the stress fields therein. Effects of a large void near a crack tip on crack initiation are also investigated by taking the shear localization into account. The critical value of the crack tip opening displacement predicted by the present investigation is shown to coincide with the published experimental data.

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Résumé On examine les effets d'une nucléation et d'une croissance de micro-cavités sur les champs de contrainte et de déformation au voisinage de l'extrémité d'une fissure en recourant au modèle constitutif de Gurson pour les solides poreux plastiques, et en utilisant une méthode par éléments finis formulée de manière à admettre des modifications importantes de géométrie. On montre que les microcavités coalescent et croissent rapidement en avant de la fissure sur une distance inférieure au diamètre qu'atteint l'arrondissement de la fissure et qu'elles ont une grande influence sur le champ de contrainte qui règne dans cette région. On étudie également l'influence d'une grande lacune au voisinage de l'extrémité d'une fissure sur l'amorçage de la cassure, en prenant en compte le cisaillement local. On montre que la valeur critique du COD à l'extrémité de la fissure telle que prédite par la présente étude coïncide avec les données expérimentales de la littérature.

     

Damage mechanics models of ductile crack growth in welded specimens

Two-dimensional, plane strain, finite element analyses of strength-mismatched welded joints have been performed using the modified boundary layer formulation. The welds were idealized as two-material joints with the material interface running parallel to the crack, which was embedded in the weld material. The Rousselier ductile damage model was employed within the weld material to simulate crack extension due to the growth and coalescence of microvoids. By analysing models with different levels of material mismatching, weld dimensions and applied T -stress levels, it was possible to analyse the effects of crack tip constraint due to both material mismatching and specimen geometry on the fracture resistance of the weld material.
The results show that material strength overmatching (where the weld material is stronger than the base material) reduces the level of constraint ahead of the crack, which can increase the resistance to fracture of the weld material. Conversely, material strength undermatching increases crack tip constraint, reducing the fracture resistance of the joint. By employing estimates for the crack tip constraint levels, Q _M , based on the applied load, level of material mismatching and weld region thickness, it has been possible to 'order' the J– resistance curves of overmatched joints by generating a family of J–Q _M loci which describe the effects of constraint on the fracture resistance of the weld material. However, it is shown that the Q _M-stress parameter is not capable of describing the effect of material strength undermatching on the fracture resistance of a joint, which can be much lower than that obtained from a high-constraint homogeneous specimen of weld material.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

A continuum damage mechanics model for crack initiation in mixed mode ductile fracture

This paper presents the development of a fracture criterion based on the postulation that the threshold condition of crack initiation in mixed mode ductile fracture is satisfied when the overall damage w in an element at the prospective direction of crack path reaches its critical value w_c. The validity of the proposed criterion is checked by predicting the fracture loads of thin aluminium plates containing an isolated crack inclined at the angle of =30, 45, 60 and 75 degrees and the predicted loads are compared satisfactorily with those determined experimentally. The analysis is performed based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors, thus providing additional proof of the consistency, applicability and versatility of the model. When the fracture loads of the mixed mode plates calculated using conventional fracture mechanics are compared with those determined using the proposed damage model, a maximum close to 30 percent over-estimation of the loads from the conventional approach is observed as opposed to within 7 percent discrepancy between the computed and measured fracture loads using the damage approach. The observation reveals the importance of including damage consideration in any ductile fracture analysis.The effect of varying damage coefficients on the fracture loads is examined and it is found that the crack initiation load decreases with the increase of anisotropic damage coefficient.     

Damage driven crack initiation and propagation in ductile metals using XFEM

Originally Continuum Damage Mechanics and Fracture Mechanics evolved separately. However, when it comes to ductile fracture, an unified approach is quite beneficial for an accurate modelling of this phenomenon. Ductile materials may undergo moderate to large plastic deformations and internal degradation phenomena which are well described by continuum theories. Nevertheless in the final stages of failure, a discontinuous methodology is essential to represent surface decohesion and macro-crack propagation. In this work, XFEM is combined with the Lemaitre ductile damage model in a way that crack initiation and propagation are governed by the evolution of damage. The model was built under a finite strain assumption and a non-local integral formulation is applied to avoid pathological mesh dependence. The efficiency of the proposed methodology is evaluated through various numerical examples.     

Detection and toughness characterisation of ductile crack initiation in 316 stainless steels

Tests on SEN bend specimens of cold worked 316 stainless steels have enabled values of the crack opening displacement at fibrous crack initiation, _v, to be compared with initiation toughness values implied by various crack monitoring techniques and methods of assessing crack tip ductility. The estimation methods available for obtaining values of the J contour integral from a load/displacement curve have been utilised and compared and have enabled relationships between J _Q, ₁ and specimen geometry to be investigated for the test materials. The results indicate that the sensitivity of the crack monitoring techniques to the detection of initiation is not only dependent on experimentation but also on the rate at which ductile crack growth proceeds following initiation. The interrelation between sensitivity, crack growth rate and toughness is discussed.

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Résumé Des essais sur des éprouvettes de flexion à entailles latérales simples en acier inoxydable 316 écroui ont permis d'établir les valeurs du COD lors de l'amorçage de fissure fibreuse, ces valeurs étant comparées avec les valeurs de la ténacité à l'amorçage déduites de diverses techniques de détection de fissuration ainsi que de méthodes pour établir la ductilité à fond d'entaille. On a utilisé les méthodes approximatives qui sont disponibles pour obtenir les valeur de l'intégrale de contour J à partir d'une courbe charge-déplacement; on a comparé et établi des relations entre J _Q, le COD et la géométrie de l'éprouvette utilisée pour les matériaux d'essai. Les résultats montrent que la sensibilité des techniques de détection d'une fissure et plus particulièrement de son initiation ne dépend pas seulement des conditions expérimentales mais également de la vitesse à laquelle la croissance de la fissure se produit après l'initiation. On discute les relations entre la sensibilité, la vitesse de croissance de la fissure et la ténacité.

     

Fatigue crack initiation in notched specimens of 17Mn4 steel

Fatigue crack initiation life is predicted for notched bend specimens with two different notch acuities and two stress ratios using the equivalent strain energy density method. The material used was 17Mn4 steel, widely applied in pressure vessel construction. The monotonic and cyclic mechanical properties and the strain-life constants were experimental determined in this work. A comparison was made between predicted and experimental lives obtained for two different optically measured crack lengths. Good agreement was obtained for stress ratios, R, of 0 and −1, and for two notch stress concentration factor values. The observed mean stress effect on crack initiation lives is well modelled in the prediction by the method used with calculation of both strain range and mean stress at the root of the notch.     

Crack initiation and propagation in ductile specimens with notches: experimental and numerical study

Failures of components and structures are often related to the presence of notches of different shapes. Damage modelling techniques have been proven capable of modelling the crack initiation and propagation in ductile materials (such as Al alloys). The Gurson–Tvergaard–Needleman (GTN) method and extended finite-element method (XFEM) are compared against original experiments to study the crack initiation and propagation processes in aluminium specimens with different notch shapes (V-shape, U-shape and square). Two regimes are considered in this study: quasi-static and impact uniaxial tensile loading. Results show that the load-bearing capability predicted with the two methods is somewhat lower compared to experiments; still, the crack shapes were predicted correctly, with the exception of the square-notch case, for which XFEM was unable to predict the correct shape due to limitations in the model formulation. This study provides information useful for the design of components with stress raisers that are exposed to different loading regimes and shows limitations in both the GTN- and XFEM-based approaches that in many cases underestimate the load-bearing capacity.     

Indirect measuring of crack growth by means of a key-curve-method in pre-cracked Charpy specimens made of nodular cast iron

The determination of dynamic crack resistance curves from single specimen fracture tests requires information about the crack advance during the experiment. Here, attention is focused on crack resistance curves for nodular cast iron based on experimental data from instrumented Charpy tests. In order to estimate the actual crack length a key curve method (KCM) is employed. On the other hand, the Charpy impact tests were realized numerically using finite element calculations in conjunction with a continuum damage model (CDM) to simulate ductile crack growth. The parameters of the CDM model were determined from the experimental data of single specimen fracture tests. Equivalence between the experimental and the numerical realization of a fracture test was ensured by validating the predictions of the numerical simulations by means of low blow fracture tests. Comparison between the crack advance predicted by the numerical simulations and the results obtained using the proposed KCM shows a sufficiently well agreement with the actual crack length. Furthermore, crack resistance curves obtained from single specimen tests using either standard estimation schemes in conjunction with the KCM or numerical simulations are compared with the predictions based on low blow fracture tests.     

On the determination of material parameters in crack initiation laws

Crack initiation along slip bands can be described by the Tanaka–Mura relation and its extensions. These relations are based on dislocation theory and determine the number of load cycles to reach a critical dislocation density for a given value of the resolved shear stress along the potential crack path. An important material parameter in these relations is the critical shear stress which is a threshold value for crack initiation, i.e. the number of cycles to crack initiation becomes infinitely high if the resolved shear stress along the potential crack path stays below this threshold value. This critical shear stress is determined using a database for microcrack initiation, microcrack growth, and coalescence obtained with a martensitic steel. The number of cracks per unit area, the so‐called crack density, was derived from this database as a function of the number of load cycles. These experimentally observed values of the crack density are compared to values obtained by simulating the crack initiation process using a random cell structure as a mesoscopic unit cell. A best fit is obtained for values of the critical shear stress between 110 and 160 MPa with the uncertainty both related to simplifications in the model and to limitations of the experimental analysis.