Prediction of ductile fracture in anisotropic steels for pipeline applications

Large diameter steel pipelines for gas transportation may experience extreme overloads due to external actions such as soil sliding, faults movements, third part interactions. In these scenarios the material undergoes severe plastic strains which locally may reach the fracture limits. Due to the manufacturing process, the steels used in such applications have an anisotropic behavior both for plasticity and fracture. In this paper two steel grades have been characterized in view of anisotropic plastic fracture. Fracture tests have been planned to characterize the fracture behavior under different stress states and in different directions to define the anisotropic sensitivity. Finite element modelling, incorporating an anisotropic plasticity formulation, has been used to calculate the local fracture parameters in the specimens and to define the complete ductile fracture locus. An uncoupled damage evolution law has been finally used to evaluate the fracture limits on real pipelines failed in full scale laboratory tests. The strain to fracture prediction has been verified by local strain measurements on the fractured pipes. The model robustness has been also verified on global parameter predictions, such us the burst pressur

An Equation of State for Anisotropic Solids under Shock Loading

An anisotropic equation of state is proposed for accurate extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked single crystals and polycrystalline alloys. The proposed equation of state represents mathematical and physical generalization of the Mie-Gr\"{u}neisen equation of state for isotropic material and reduces to this equation in the limit of isotropy. Using an anisotropic nonlinear continuum framework and generalized decomposition of a stress tensor [Int. J. Plasticity \textbf{24}, 140 (2008)], the shock waves propagation along arbitrary directions in anisotropic solids of any symmetry can be examined. The non-associated strength model includes the distortion effect of the yield surface which can be used to describe the anisotropic strength differential effect. A numerical calculation showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental data. The results are presented and discussed, and future studies are outlined.Comment: 6 pages, 2 figure

Anisotropic yield functions in a co-rotating reference frame

In metal forming simulations large deformations are often treated based on objective formulations. Large rotations are accounted for by rotating the stress tensor or approximating the rotation by some integration rule for the rate of rotation. For isotropic material behavior, this is easily done. For anisotropic material behavior however, not only the stresses, but also the relation between stress rate and strain rate must be updated. In this case it is easier to take a co-rotating reference frame and apply the constitutive relations on a strain measure that is neutralized for rigid body translations and rotations. This paper presents an algorithm that is based on the latter idea. The algorithm directly uses the increments in the deformation gradient, avoiding as much as possible to take time derivatives that should then be integrated subsequently. The algorithm is applied to a constitutive model including an initial anisotropic yield function and isotropic and kinematic hardening. The kinematic hardening makes use of a maximal back stress surface [1] to account for behavior observed in cyclic loading

Unified anisotropic elastoplastic model for sand

This paper presents a unified approach to model the influence of fabric anisotropy and its evolution on both the elastic and plastic responses of sand. A physically based fabric tensor is employed to characterize the anisotropic internal structure of sand. It is incorporated into the nonlinear elastic stiffness tensor to describe anisotropic elasticity, and is further included explicitly in the yield function, the dilatancy relation, and the flow rule to characterize the anisotropic plastic sand response. The physical change of fabric with loading is described by a fabric evolution law driven by plastic strain, which influences both the elastic and the plastic sand behavior. The proposed model furnishes a comprehensive consideration of both anisotropic elasticity and anisotropic plasticity, particularly the nonlinear change of elastic stiffness with the evolution of fabric during the plastic deformation of sand. It offers a natural and rational way to capture the noncoaxial behavior in sand caused by anisotropy. It also facilitates easy determination of the initial anisotropy in sand based on simple laboratory tests and avoids the various arbitrary assumptions on its value made by many previous studies. The model predictions on sand behavior compare well with test data

Identification of nonlinear kinematic hardening parameters for sheet metal from biaxial loading tests

In this work an anisotropic material model at finite strains with nonlinear mixed (isotropic and kinematic) hardening is used for the identification of the hardening parameters of sheet steel. The algorithmic system is thereby reduced to a single equation return mapping. For the identification, a cruciform specimen is loaded biaxially in an alternating shear test to provoke the kinematic hardening behavior and prevent the sheet from buckling. The material parameters are found through an optimization strategy by comparing the deformation field from the experiment to that from a finite element (FE) simulation. The resulting cost function is minimized by means of a gradient-based method

Numerical integration of the incrementally non-linear, zero elastic range, bounding surface plasticity model for sand

SANISAND-Z is a recently developed plasticity model for sands with zero purely elastic range in stress space within the framework of Bounding Surface (BS) plasticity. As a consequence of zero elastic range the plastic strain increment direction, and consequently the elastic-plastic moduli fourth order tensor depends on the direction of the stress increment, rendering the model incrementally non-linear and intrinsically implicit. An iterative algorithm based on the Backward Euler method is presented to solve the non-linear system of ordinary differential equations. A non-traditional consistency condition based on the plastic multiplier is introduced as a core element of the system. A thorough analysis of the stability and accuracy of the algorithm is presented based on error estimation. The proposed integration scheme allows the use of SANISAND-Z framework in Finite Element Analysis

Time-independent Anisotropic Plastic Behavior by Mechanical Subelement Models

The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the iscoplasticity-theory

On the Rate-dependent Plasticity Modelling of Unidirectional Fibre-reinforced Polymeric Matrix Composites

Three different approaches to plasticity are investigated to model the experimentally-observed non-linear behaviour of unidirectional fibre-reinforced polymeric matrix materials. The first and simplest approach consists on assuming independent one-dimensional rate-dependent plasticity on in-plane (12) and through-thickness longitudinal (13) shear components of the Cauchy stress tensor. The second, employs a 3D extension of the plane stress Hill'48 anisotropic plastic surface. The third and the last is formulated as a quadratic yield function inspired by Puck's fracture initiation criterion. It searches for a plastic localisation plane in which a certain combination of normal and shear stresses is maximum. Numerical simulations are conducted to analyse the off-axis compression behaviour of carbon fibre reinforced epoxy composite under varying loading rates. The afore-mentioned three different approaches are explored with an aim to predict the experimentally-observed non-linear response of such composites. The model parameters are determined using a deterministic inverse modelling strategy employing an iterative domain reduction optimisation technique. As far as the experiments are concerned, the quasi-static and medium rate tests were carried out in universal testing machines, while the experiments at high rate were conducted in a Split Hopkinson Pressure Bar system. The effectiveness in terms of accuracy and robustness of the three approaches are discussed