Multi-surface failure criterion for saline ice in the brittle regime

In this paper, the development of a 3-D failure criterion for saline ice is presented. The need for such general 3-D failure formulation stems from the fact that, during ice–ship interactions, ice undergoes a complex state of deformation and stress before it fails and breaks away, and the use of the uniaxial strength of ice to compute impact ice loads may lead to inaccurate load calculations and non-conclusive results.In recent years, with the availability of High Power Computers (HPC), numerical methods are being used more than ever before in marine and ice engineering problems. Numerical models based on computational techniques such as finite elements, boundary elements and discrete elements require 3-D constitutive models and failure criteria to represent the behavior of the materials involved (such as the behavior of the ship structure, ice and water “fluid”).At high-speed impacts (strain rates >10⁻³ s⁻¹), ice behaves as a linear elastic material with a brittle mode of failure. Previously, Derradji-Aouat [Derradji-Aouat, A., 2000. A unified failure envelope for isotropic freshwater ice and iceberg ice. ASME/OMAE-2000, Int. Conference on Offshore Mechanics and Arctic Engineering, Polar and Arctic section, New Orleans, US, PDF file # OMAE-2000-P/A # 1002] developed a unified 3-D failure envelope for both fresh water isotropic ice and iceberg ice. In this paper, that formulation is extended to include failure of saline ice (in addition to fresh water ice and iceberg ice). The results of a significant number of true triaxial tests using Laboratory Grown Ice (LGSI) were obtained from the open literature. The results of these tests formed a database that enables the existing failure model [Derradji-Aouat, A., 2000. A unified failure envelope for isotropic freshwater ice and iceberg ice. ASME/OMAE-2000, Int. Conference on Offshore Mechanics and Arctic Engineering, Polar and Arctic section, New Orleans, US, PDF file # OMAE-2000-P/A # 1002] to be extended from the isotropic fresh water ice and iceberg ice to columnar saline ice.Mroz's [J. Mech. Phys. Solids 15 (1967) 163] concept for the multi-surface failure theory is used in both studies (the present study, for saline ice, as well as in the previous study, for the fresh water isotropic ice and iceberg ice). It appears that the same set of the equations is applicable to the failure of all three types of ice. The possibility of the existence of a universal and general failure criterion for all types of ice is discussed.The validation of the present multi-surface failure criterion was discussed on the basis of comparisons between predicted failure curves and actual true triaxial test results. An overall discrepancy of predicted versus measured strength values of less than 20% was calculated.     

Extension of strain–life equation for low‐cycle fatigue of sheet metals using anisotropic yield criteria and distortional hardening model

The fatigue strain–life equation is in general applicable to isotropic materials. It was recently attempted to account for material anisotropy because of crystallographic texture in fatigue modelling. The proposed modification was limited to isotropic hardening. The present work is an extension of the previous work, wherein a general framework to model anisotropy using phenomenological yield criterion and anisotropic hardening is provided. Yld2004‐18p yield criterion and the so‐called homogenous anisotropic hardening model are used to demonstrate the anisotropic cyclic behaviour of low carbon steel. The proposed methodology can be utilized in applications including multiaxial fatigue modelling.     

Analytical modeling of fatigue crack propagation in metals coupled with elasto-plastic deformation

In the present investigation, the G _max criterion, which is based on the elastic strain energy principle, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the plastic strain energy and, hence, a new elasto-plastic energy-based model is presented. Subsequently, the proposed model is employed to predict fatigue crack growth in rectangular steel plates under complex stress states. The results obtained using the elasto-plastic energy model proposed are compared with those obtained using the commonly used Paris law and our experimental data.     

Non-orthogonal stress modes for interfacial fracture based on local plastic dissipation

Interfacial cracks have several features which are different from those of cracks in homogeneous materials. Among those, the loading mode dependency of interfacial toughness has been a main obstacle to the widespread utilization of interfacial fracture mechanics. In this study, plasticity-induced toughening of an interface crack between an elastic–plastic material and an elastic material is studied. A useful relationship between the plastic dissipation and the plastic zone size is derived via an effective crack length model. Non-orthogonal stress modes for interface cracks are proposed on the basis of the plastic dissipation mechanism and a mixed-mode criterion for interfacial crack growth is also proposed using these stress modes. The non-orthogonal stress modes are able to represent the asymmetric behavior, mode-dependent toughening and ε-dependency of interfacial crack growth.     

MODELLING FOR TRANSCRYSTALLINE AND INTERCRYSTALLINE FRACTURE BY VOID NUCLEATION AND GROWTH

A criterion has been formulated for transcrystalline and intercrystalline fracture caused by the evolution of voids located both in a grain and on grain boundaries. The criterion is based on the idea of plastic collapse for a unit cell that is a regular structural mezovolume of polycrystalline material. The criterion does not require the introduction of any empirical parameters, such as critical void size, critical size of ligament between voids and critical void volume fraction, which are used in most models.
Modelling has been performed for void nucleation and growth in a grain and on grain boundaries for elastic–plastic deformation and under creep conditions. A scheme is proposed to describe the transition from transcrystalline to intercrystalline cavitation fracture as a function of strain rate and temperature.
The effect of stress triaxiality on the critical strain and the lifetime for both transcrystalline and intercrystalline fracture has been investigated. A comparison of the results predicted by the suggested criterion with available empirical data has been performed.     

A modified plasticity theory for porous metals

A plasticity theory for porous metals is proposed. A simple model of a porous materials is analysed by the finite element method. Small strain elastic–plastic analysis provides stress–strain curves, yield stressed and incremental plastic strain vectors for different void ratios. An assessment is made of an existing yield criterion for porous metals. A modified yield criterion and plastic potential function and, consequently, different plasticity equations are given. Reasonable agreement is obtained between the present numerical results and previous results in the literature.     

Non-orthogonal stress modes for interfacial fracture based on local plastic dissipation

Interfacial cracks have several features which are different from those of cracks in homogeneous materials. Among those, the loading mode dependency of interfacial toughness has been a main obstacle to the widespread utilization of interfacial fracture mechanics. In this study, plasticity-induced toughening of an interface crack between an elastic-plastic material and an elastic material is studied. A useful relationship between the plastic dissipation and the plastic zone size is derived via an effective crack length model. Non-orthogonal stress modes for interface cracks are proposed on the basis of the plastic dissipation mechanism and a mixed-mode criterion for interfacial crack growth is also proposed using these stress modes. The non-orthogonal stress modes are able to represent the asymmetric behavior, mode-dependent toughening and ε-dependency of interfacial crack growth.     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.     

Model tests of iceberg towing

Icebergs may cause a threat to offshore installations, vessels and operations in a number of Arctic regions. In order to increase the understanding of what happens when an iceberg tow is started in ice covered waters; physical tank model tests have been carried out in various concentrations of sea ice. The objectives with these tests have been to evaluate the practical arrangements for iceberg towing and to collect data regarding tow loads and iceberg behaviour during the tow.The tank model tests were carried out in scale 1:40 in the ice tank at Hamburg Ship Model Basin (HSVA), Germany. Two different iceberg models were used and each towed in four different ice concentrations. From all tests, tow line forces, iceberg displacements and rotations were recorded.It was concluded that towing in 50% ice concentrations and higher were not realistic due to high resistance. During the tows in high concentrations, ice was breaking in flexural mode, crushing, rafting and ridging continuously in front of the iceberg models. With respect to the tow line, the line was fully extended and lifted up from the water/ice. In real operations this may increase the risk for tow line rupture and subsequent “snapping”. In 50% ice concentration, total loads in the tow line will most of the time be lower than maximum bollard pull for powerful diesel electric icebreakers indicating that towing up to this concentration may be feasible. However, tow lines will have to resist even the highest peak loads during a tow and it is unclear whether sufficiently strong tow lines can be produced. With respect to tows in 20% concentration and open water, loads are significantly lower indicating that towing in low ice concentrations should be feasible.Measured loads seem to be reasonable well described by a log-normal distribution. The concentrations of surrounding sea ice are found to be most important for the load magnitude while variations in speed, acceleration, course and iceberg shape seem to be less important.A log-normal distribution, in which the parameters are functions of the sea ice concentration, has been fitted to recorded data. Combined with information regarding expected tow length, this distribution may be applied in order to provide crude estimate on extreme loads during an iceberg tow. By performing additional model tows in different ice conditions and with larger variations in iceberg size, this model may be further developed to be applicable in a wide range of scenarios.     

Three-dimensional analyses of plastic constraint for through-thickness cracked bodies

A three-dimensional strip yield model has been proposed to rationalize effects of out-of-plane and in-plane constraints. By use of the model, plastic constraints around a straight-through crack in finite thick plates made of strain hardening materials are analyzed. A global constraint factor α is defined to simulate the three-dimensional effects in two-dimensional analysis. Effects of thickness and stress states on the size of crack-tip plastic zone and α are studied in detail. A unique variation curve of α against normalized thickness is obtained for different combination of materials, load levels and geometry. Influences of the in-plane constraint on the α-thickness curve are analyzed as well. It is shown that the influence of T-stress can be considerable only if the plastic-zone size becomes comparable to the crack length. The difference between the present results and Newman, Bigelow and Shivakumer's three-dimensional finite element results is within 6% over a large range of thickness and stress levels. The three-dimensional shape of the plastic zone is discussed as well. Potential applications of the model are discussed and it is shown by an example that the present model can be used to explain the effects of thickness upon fatigue crack growth.     

高体积含量颗粒增强复合材料的一个细观力学模型Ⅱ: 弹塑性与损伤分析

在高体积含量颗粒增强复合材料细观弹性分析的基础上, 引入了细观塑性和细观损伤模型: 基体用服从Von Mises 屈服准则的理想弹塑性材料模拟, 用沿圆柱形基体轴线方向的平均应力(即对称面上的应力) 来判断基体的屈服, 并将基体的塑性部分简化为圆柱状轴对称区域。建立了基体和颗粒/ 基体界面统一的损伤准则, 该准则同时考虑了最大应变和三轴应力的影响, 通过对细观塑性和细观损伤在空间取向上的平均, 建立了材料宏观模量的折减法则。用该细观力学模型, 数值模拟了一种实际金属基复合材料的强度实验, 理论模型与实验结果吻合。      

Size effects in phenomenological strain gradient plasticity constitutively involving the plastic spin

In the small deformation range, we consider and discuss the phenomenological (or isotropic) “higher-order” theory of strain gradient plasticity put forward in Section 12 of Gurtin [1], which includes the dissipation due to the plastic spin through a material parameter called χ. In fact, χ weighs the square of the plastic spin rate into the definition of an effective measure of plastic flow peculiar of the isotropic hardening function. Such a model has been identified by Bardella [2] as a good isotropic approximation of a crystal model to describe the multislip behaviour of a single grain, provided that χ be set as a specific function of other material parameters involved in the modelling, including the length scales. The main feature of the underlying gradient approach is the accounting for both dissipative and energetic strain gradient dependences, with related size effects. The dissipative strain gradients enter the model through the definition of the above mentioned effective measure of plastic flow, whereas the energetic strain gradients are involved in the modelling by defining the defect energy, a function of Nye’s dislocation density tensor added to the free energy to account for geometrically necessary dislocations (see, e.g., Gurtin [1]). By exploiting the deformation theory approximation, we apply the model to a simple boundary value problem so that we can discuss the effects of (a) the criterium derived by Bardella [2] for choosing χ and (b) non-quadratic forms of the defect energy. We show that both χ and the nonlinearity chosen for the defect energy strongly affect quality and magnitude of the energetic size effect which is possible to predict.     

Long-term iceberg collision-risk assessment methods for fixed offshore structures

This study shows that iceberg collision-risks for fixed offshore structures in the Arctic are often heavily underestimated at present. The study concentrates on concepts for the mathematical modelling of the probability of an iceberg hitting a fixed offshore structure in the Arctic. Simple and verifiable assumptions provide extensive statements of this risk. A fractal model for iceberg production is used. An iceberg melting and breakdown model is formulated and its risk implications are derived by analysing iceberg tracks by geometrical methods. Some numerical results from data analyses and simulations are presented. This work is intended to be a contribution to the discussion on ‘engineering standards’ and indicate where attention is required when carrying out data acquisition programs in the Arctic.     

Singular crack-tip fields for pressure sensitive plastic solids

Plain strain mode-I singular plastic fields are examined for cracks embedded in pressure sensitive solids. Material response is described by a small strain deformation theory in conjunction with elliptic yield criterion and plastic potential. Non-associativity is accounted for and a pure power law is assumed to characterize strain hardening. The material does not admit a strain energy function hence it is not possible to deduce a-priori the J-integral motivated stress singularities. A standard separation of variables representation of near-tip eigenfunctions has been evaluated numerically, over a range of material parameters. It has been found that stress singularities may deviate from J-integral predictions, with increasing non-associativity, by up to nearly 20%. Sample illustrations are provided for singular field profiles and some aspects of pressure sensitive non- associated plasticity are discussed.     

On the plastic zone and residual stresses within a strip and a half plane under a moving load

A quasi-steady solution has been obtained for the determination of the extent of plastic zones and the amplitude of the residual stresses in (1) an elasto-plastic strip lying on a rigid frictionless base and (2) a half-plane, under the first passage of a moving load. The load is assumed to be applied with a semi-elliptic pressure distribution which is of sufficient magnitude to cause plastic yielding in the body. A work-hardening material obeying von-Mises' yield criterion is considered. A numerical solution procedure, based on discretizing the plastic strain field in the coordinate system moving with the load into uniformly strained rectangular or semi-infinite elements has been developed. Numerical results are obtained for a strip with linear work-hardening material properties. The effect on the distribution of residual stresses created by the ratio of load half-width to strip thickness is also discussed.     

DEVELOPMENT OF A CONSTITUTIVE MODEL FOR BIAXIAL LOW-CYCLE FATIGUE

Abstract— A version of the endochronic theory of plasticity for the modelling of nonproportional cyclic loading has been developed. To describe an additional hardening of a material a new engineering method for defining a nonproportionality parameter is proposed for a wide class of cyclic strain paths with a prescribed maximum range of plastic or total strains. This parameter makes it possible to establish an unambiguous linear dependence between the cyclic strain path shape and the stress level in a stabilized state. Conjugation conditions have been formulated to describe complex histories of nonproportional cyclic loading. The results of the modelling are shown to be in fair agreement with the experimental data.     

Stress triaxiality effect on void nucleation in ductile metals

The stress triaxiality effect on the strain required for void nucleation by particle‐matrix debonding has been investigated by means of micromechanical modelling. A unit‐cell model considering an elastic spherical particle embedded in an elastic‐plastic matrix was developed to the purpose. Particle‐matrix decohesion was simulated through the progressive failure of a cohesive interface. It has been shown that the parameters of matrix‐particle cohesive interface are correlated with macroscopic material properties. Here, a simple relationship for the maximum cohesive opening at interface failure as a function of material fracture toughness and yield stress has been derived. Results seem to confirm that, increasing stress triaxiality, the strain at which void nucleation is predicted to occur decreases exponentially in a similar way as for fracture strain. This result has substantial implications in modelling of ductile damage because it indicates that if the stress triaxiality is high enough, ductile fracture can occur at plastic strain lower than that necessary to nucleate damage for moderate or low stress triaxiality regime.     

Numerical modelling of the structural behaviour of thin-walled cast magnesium components using a through-process approach

A through-process methodology for numerical simulations of the structural behaviour of thin-walled cast magnesium components is presented. The methodology consists of casting process simulations using MAGMAsoft, mapping of data from the process simulation onto a FE-mesh (shell elements) and numerical simulations using the explicit FE-code LS-DYNA. In this work, generic High Pressure Die Cast (HPDC) AM60 components have been studied using axial crushing, 3-point bending and 4-point bending tests. The experimental data are applied to obtain a validated methodology for finite element modelling of thin-walled cast components subjected to quasi-static loading. The cast magnesium alloy is modelled using a user-defined material model consisting of an elastic–plastic model based on a modified J2-flow theory and the Cockcroft–Latham fracture criterion. The fracture criterion is coupled with an element erosion algorithm available in LS-DYNA. The constitutive model and fracture criterion are calibrated both with data from material tests and data from the process simulation using MAGMAsoft.     

Monte Carlo calculations of iceberg draft changes caused by roll

Draft changes in iceberg roll have been investigated using a Monte Carlo technique for generating iceberg shapes of constant, polygonal cross section. Stability is assessed from the potential energy curves calculated assuming vertical but not rotational hydrostatic equilibrium. No modelling of the roll dynamics has been included. The draft changes are approximately normally distributed, with increases almost as probable as decreases. Extreme draft changes (defined to be those in excess of 20%) are not uncommon. The mean draft change, standard deviation, skewness and kurtosis depend on the number of sides in the berg model, and on the ratio of berg ice density to seawater density. In particular the fraction of extreme draft changes is a sensitive function of this ratio.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.