Christian Thaulow

A complete Gurson model approach for ductile fracture

Abstract Recently, a complete Gurson model has been introduced by the authors. The complete Gurson model is a combination of the modified Gurson model which deals with microvoid nucleation and growth, and a physical microvoid coalescence criterion based on the plastic limit load model by Thomason. By comparing finite element cell modeling analyses, the complete Gurson model is accurate for both non-hardening and hardening materials. One attractive feature of the complete Gurson model is that material ductile failure is exclusively linked to the microvoid nucleation parameter, and the nucleation parameter in many cases can be determined without metallurgical examinations. Furthermore, the so-called critical void volume fraction fc, has been eliminated from material constants. In this paper, two simple microvoid nucleation models for modeling ductile fracture are discussed, and a method which applies multitension specimens including both smooth and notched cylindrical specimens for determining the microvoid nucleation parameter is introduced. Once the microvoid nucleation parameter has been determined from the tension specimens, the characteristic length parameter which describes the stress/strain gradient effect can be fitted from fracture mechanics tests. Material ductile crack resistance behavior is then a function of the microvoid nucleation parameter, the length parameter and the specimen geometry. For modified boundary layer models, it has been found that the crack resistance curves can be normalized by the T stress, and the T stress can be possibly taken as the geometry controlling parameter for ductile crack growth.

Determining material true stress-strain curve from tensile specimens with rectangular cross-section

Abstract The uniaxial true stress logarithmic strain curve for a thick section can be determined from the load–diameter reduction record of a round tensile specimen. The correction of the true stress for necking can be performed by using the well-known Bridgman equation. For thin sections, it is more practical to use specimens with rectangular cross-section. However, there is no established method to determine the complete true stress–logarithmic strain relation from a rectangular specimen. In this paper, an extensive three-dimensional numerical study has been carried out on the diffuse necking behaviour of tensile specimens made of isotropic materials with rectangular cross-section, and an approximate relation is established between the area reduction of the minimum cross-section and the measured thickness reduction. It is found that the area reduction can be normalized by the uniaxial strain at maximum load which represents the material hardening and also the section aspect ratio. Furthermore, for the same material, specimens with different aspect ratio give exactly the same true average stress–logarithmic strain curve. This finding implies that Bridgmans correction can still be used for necking correction of the true average stress obtained from rectangular specimens. Based on this finding, a method for determining the true stress–logarithmic strain relation from the load–thickness reduction curve of specimens with rectangular cross-section is proposed.

Alpha-Helical Protein Networks Are Self-Protective and Flaw-Tolerant

Alpha-helix based protein networks as they appear in intermediate filaments in the cell’s cytoskeleton and the nuclear membrane robustly withstand large deformation of up to several hundred percent strain, despite the presence of structural imperfections or flaws. This performance is not achieved by most synthetic materials, which typically fail at much smaller deformation and show a great sensitivity to the existence of structural flaws. Here we report a series of molecular dynamics simulations with a simple coarse-grained multi-scale model of alpha-helical protein domains, explaining the structural and mechanistic basis for this observed behavior. We find that the characteristic properties of alpha-helix based protein networks are due to the particular nanomechanical properties of their protein constituents, enabling the formation of large dissipative yield regions around structural flaws, effectively protecting the protein network against catastrophic failure. We show that the key for these self protecting properties is a geometric transformation of the crack shape that significantly reduces the stress concentration at corners. Specifically, our analysis demonstrates that the failure strain of alpha-helix based protein networks is insensitive to the presence of structural flaws in the protein network, only marginally affecting their overall strength. Our findings may help to explain the ability of cells to undergo large deformation without catastrophic failure while providing significant mechanical resistance.

Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.

Efficient fracture assessment of pipelines. A constraint-corrected SENT specimen approach

Abstract Reeling has proven to be an efficient and cost effective method for offshore pipelaying. During the reeling process the pipe undergoes deformation that can strain the material by 1–2%. The existing failure assessment methods often turn out to be too conservative to allow such a strain level in the structure. The amount of conservatism can be significantly reduced by using a new failure assessment approach developed by SINTEF. This approach depends on finite element calculations for establishing the non-linear fracture mechanics parameters and the stress and strain distributions in the pipe. The present study addresses the performance of shell and line spring finite elements as a cost effective tool for performing such numerical calculations.

Effects of crack size and weld metal mismatch on the has cleavage toughness of wide plates

Abstract The heat affect zone (HAZ) is in many cases considered to be the most critical part of a weldment. In this paper, the effect of crack size and weld metal mismatch on the HAZ cleavage toughness of wide plate specimens with X-groove has been investigated by the J-Q-M theories and a simple micromechanism for cleavage fracture. Two crack sizes have been studied ( a w = 0.1 and 0.3). In the analyses, the HAZ yield strength is assumed to be higher than the base metal. For each crack size, weld metal local overmatch and local evenmatch with respect to the HAZ are considered. For a given global strain, the results indicate that weld metal overmatch and evenmatch yield the same crack tip loading in terms of J-integral for a w = 0.3 . For a w = 0.1 , overmatch gives lower crack tip loading than evenmatch. For a given crack tip loading, weld metal local evenmatch in general results in less effective crack tip loading than the overmatch. Overmatch is detrimental to HAZ toughness, but this detrimental effect becomes less significant when the crack size decreases.

A study on determining true stress–strain curve for anisotropic materials with rectangular tensile bars

Recently, a method has been proposed for determining material true stress–strain curve with rectangular tensile bars up to localized necking. In the proposed method, material true stress–strain curve can be directly calculated from the load versus thickness reduction (at the minimum cross-section) curve. The method was established based on the finite element (FE) analysis for isotropic materials. In this study, this method has been extended for materials with isotropic elastic properties but anisotropic plastic properties. Two cases, transverse anisotropy and planar anisotropy, have been considered. Hill’s anisotropic material model implemented in abaqus was applied for the study. More than 30 three-dimensional FE analyses of rectangular specimens with different anisotropy value, hardening exponent and cross-section aspect ratio have been carried out. It is shown that the relation between thickness reduction and total area reduction of a given cross-section is influenced by material plastic anisotropy. It is, however, found that the anisotropic effect on the thickness–area reduction relation can be normalized by the width to thickness strain increment ratio r, and a modified thickness–area reduction relation is proposed and numerically and experimentally verified. One practical problem in tensile test is that it is difficult to predict the necking location. In this regard, a study on the sensitivity of initial notch geometry has been carried out. It is found that for a fixed initial notch radius, the percentage of error is approximately equal to the percentage of initial width reduction. The accuracy of using large initial width reduction can be improved by using large notch radius.

A notched cross weld tensile testing method for determining true stress–strain curves for weldments

Abstract Cross weld tensile testing is widely used in the industry to qualify welds. In these conventional testing fracture load is measured and the location of fracture (weld metal, base metal or heat affected zone) is evaluated. Because the load-elongation curve depends on the location of fracture and the initial gauge length, it cannot be utilized in the failure assessment of weldments. Failure assessment of weldments requires input of true stress–strain behaviour for each material zone. In this paper, a notched cross weld tensile testing method is proposed for determining the true stress–strain curve for each material zone of a weldment. In the proposed method, cylindrical cross weld tensile specimens, with a notch located either in the weld metal, base metal or possibly heat affected zone are applied. Due to the notch, plastic deformation is forced to develop in the notched region. A load versus diameter reduction curve is recorded. It has been shown that the true strain at maximum load is independent of the notch geometry. Furthermore, the materials true stress–strain curve can be determined from the recorded load versus diameter reduction curve of a notched cross weld tensile specimen by dividing a geometry-factor G, which is approximated by a quadratic function of the specimen diameter to notch radius ratio and a linear function of the true strain at the maximum load. It is found that G is independent of the material zone length when the homogenous material length is larger or equal to the minimum diameter.

APPLICATION OF LOCAL APPROACH TO INHOMOGENEOUS WELDS. INFLUENCE OF CRACK POSITION AND STRENGTH MISMATCH

Abstract In steel welds there is often a large variation in fracture toughness and mechanical properties between the weld metal, base material and the various heat affected zone (HAZ) microstructures. The stress field in front of a crack in a weldment can be noticeably affected by the strength mismatch between the weld metal, HAZ and the base material. The crack position relative to the various microstructures will clearly influence the strength mismatch effect. In this paper the influence of crack tip positioning on the fracture performance of strength mismatched steel welds has been studied both experimentally and by FEM analysis. For a mismatched weld with local brittle zones small changes in crack tip location can give considerable changes in the fracture performance of a CTOD specimen. A high degree of strength mismatch increases the effect of crack positioning. Weld metal overmatch increases the stress level in the heat affected zone due to material constraint and thereby reduces the cleavage fracture resistance of the weldment when the coarse grained HAZ (CGHAZ) controls the fracture. The detrimental effect of high overmatch is most pronounced for specimens with notch position at fusion line and a short distance into the brittle CGHAZ. The Weibull stress has been shown to be a suitable fracture parameter in the case where one microstructure clearly controls the cleavage fracture and the calculation of the Weibull stress therefore can be limited to this zone.

Microstructure provides insights into evolutionary design and resilience of Coscinodiscus sp. frustule

Significance Diatoms are unicellular algae that form an intricate silica cell wall. A protective shell that is light enough to prevent sinking while simultaneously offering strength against predators is of interest to the design of lightweight structural materials. Using three-point bending experiments, we show that the diatom shell has the highest specific strength of all previously reported biological materials. Fracture analysis and finite element simulations also suggest functional differentiation between the shell layers and features to mitigate fracture. These results demonstrate the natural development of architecture in live organisms to simultaneously achieve light weight, strength, and structural integrity and may provide insight into evolutionary design. We conducted in situ three-point bending experiments on beams with roughly square cross-sections, which we fabricated from the frustule of Coscinodiscus sp. We observe failure by brittle fracture at an average stress of 1.1 GPa. Analysis of crack propagation and shell morphology reveals a differentiation in the function of the frustule layers with the basal layer pores, which deflect crack propagation. We calculated the relative density of the frustule to be ∼30% and show that at this density the frustule has the highest strength-to-density ratio of 1,702 kN⋅m/kg, a significant departure from all reported biologic materials. We also performed nanoindentation on both the single basal layer of the frustule as well as the girdle band and show that these components display similar mechanical properties that also agree well with bending tests. Transmission electron microscopy analysis reveals that the frustule is made almost entirely of amorphous silica with a nanocrystalline proximal layer. No flaws are observed within the frustule material down to 2 nm. Finite element simulations of the three-point bending experiments show that the basal layer carries most of the applied load whereas stresses within the cribrum and areolae layer are an order of magnitude lower. These results demonstrate the natural development of architecture in live organisms to simultaneously achieve light weight, strength, and exceptional structural integrity and may provide insight into evolutionary design.