A review on the strain rate dependency of the dynamic viscoplastic response of FCC metals

The response of structures and materials subject to impulsive loads remains a field of intense research. The dynamic loading and temperature increase affect the material’s mechanical/failure response. For example, strains due to explosive blast will increase at rates from 10² to 10⁴ s⁻¹, leading to regimes of elastic/plastic wave propagation, plane stress and adiabatic deformations. Few constitutive models consider high strain rate effects, however some constitutive approaches that were developed and tested at low strain rate regimes will also be addressed here due to their relevance. Specific reference will be made to strain rate regimes close to 10⁴ s⁻¹, where shock waves may develop. The paper focuses on constitutive models for polycrystalline face-centred-cubic (FCC) metals since their behaviour under high strain rate regimes is not yet fully understood mostly due to path loading dependency. Reference is also made to aluminium alloys since they are widely used in virtually all fields of industry and in armour and protective structures and systems. A basic review of the main theoretical aspects that constitute the basis for most of the constitutive models described is also presented and the main features of each model are thoroughly discussed.     

Comparison of three real time techniques for the measurement of dynamic fracture initiation toughness in metals

Three techniques for measuring dynamic stress intensity factor time histories of dynamically loaded stationary mode-I cracks are compared as applied to dynamically loaded pre-cracked 6Al-4V titanium alloy specimens. The three techniques are crack opening displacement (COD), dynamic strain gage measurement, and coherent gradient sensing (CGS). The stress intensity factor histories are inferred from each measurement technique and are used to obtain the critical dynamic initiation toughness as a function of loading rate (). There are significant differences in implementation and information obtained from each of the three measurement techniques, though for the tests performed all are found to yield very similar results.     

A 50‐year retrospective review of three‐dimensional effects at cracks and sharp notches

This review is a brief survey of three‐dimensional effects at cracks and sharp notches. The overall aim is to review developments over the past 50 years leading up to the current state of the art. The review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack or notch tip. It is also restricted to static loading and to constant amplitude fatigue loading. An enormous amount of theoretical and experimental information relevant to three‐dimensional effects has been published in the past five decades, so the review is, of necessity, highly selective. Theoretical topics covered are linear elastic fracture mechanics, including Volterra distorsioni, stress intensity factors, corner point singularities, crack front line tension, displacement analysis of cracks and notches, and through thickness distributions of stresses and stress intensity factors. Crack path topics covered are fatigue crack path constraints, determination of fatigue crack paths, oscillating crack fronts in thin sheets and the transition to slant crack propagation in thin sheets. Plane strain fracture toughness testing, including standards, is covered. Overall, it can be concluded that the existence of three‐dimensional effects at cracks and sharp notches has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three‐dimensional effects numerically in detail. Despite increased understanding, three‐dimensional effects are sometimes ignored in situations where they may be important.     

Comparison of dynamic initiation toughness measured by strain gauges and the shadow optical method

The deformation and fracture behaviour in dynamically loaded Charpy specimens of BS11 rail steel were studied by two different measuring techniques. The transient records obtained from straingauges were compared with results obtained simultaneously by the shadowoptical method. Good agreement was obtained when measuring and comparing the stress intensity factor K in the initial stages of deformation behaviour prior to crack initiation. During fast fracture, the shadow optical method indicated the influence of dynamic effects on crack propagation.     

A review of deformation and fatigue of metals at small size scales

Mechanical devices are being introduced whose size scale is well below that of conventional mechanical test specimens. The smallest devices have sizes in the nanometer range, though a good proportion of structural devices are of the micrometer scale. Development of these products raises the question of how their mechanical behaviour and reliability may be predicted. Conventional macroscopic test data can be used, but these are obtained using specimens whose size is much larger than the devices themselves. There is a risk that performance predictions will be inaccurate, due to the existence of size effects. This paper covers small size scale testing in metallic specimens and devices, concentrating on free‐standing specimens. To begin, some examples of micro‐scale devices are given. Fabrication methods for small metallic devices are then briefly described. This is followed by a review of experimental observations of mechanical properties in various metallic materials at the micro‐scale, highlighting the differences in results from different research groups and the gaps in our current knowledge. A section on computational and predictive modelling is included, in recognition of the role of modelling in device design and testing. Overall, the findings are that size effects are common, particularly in crystalline samples when the grain size is similar to one or more of the specimen dimensions. However, observations of size effects differ between studies and mechanical properties can vary widely, even for the same type of material. As a consequence, the relationships between specific device processing methods, specimen size and material properties must be adequately understood to ensure successful performance.     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

A general linear method to evaluate the hardening behaviour of metals at large strain with full‐field measurements

The hardening behaviour of metals is generally described in terms of a stress‐strain curve derived from experiments. In this paper, a linear method to identify the stress‐strain curve starting from full‐field measurement data is presented. This method can be applied to any stress state using a generic yield function, the only requirement is that the full‐field measurement is extended up to the border of the specimen. The method is presented and validated using a finite element model of a notched specimen. Moreover, experiments were performed on specimens cut from a BH340 steel sheet to illustrate the viability to actual cases. Two geometries were considered, a standard uniaxial test, where the method was used to evaluate the post‐necking behaviour, and a notched specimen with a heterogeneous strain field. The proposed method, named linear stress‐strain curve identification (LSSCI), can be a useful tool in combination with inverse methods to identify the constitutive behaviour of metals in large strain plasticity.     

A note on the arrangement of strain gauges and the sensitivity of strain measurement

A discussion for investigating the yield surface of metal is described. The paper also presents the discussions of the accuracy of strain measurements and the arrangement of three–element 45° strain gauges on a thin–walled tube under combined loadings.     

A method for determining dynamic stress intensity factors from cod measurement at the notch mouth in dynamic tear testing

A formula is derived for determining dynamic stress intensity factors directly from crack mouth opening displacements in dynamic tear test specimen. The results obtained by the present estimation method for stationary as well as propagating cracks agree excellently with those directly obtained through a highly accurate moving-singularity finite element method. The present method can also be applied for other types of specimen which have a relatively short edge crack without any loading on the crack surface. The present simple estimation method should be of great value in the experimental measurement of dynamic stress-intensity factors for propagating cracks in (opaque) structural steel dynamic tear test specimens.     

Full-field measurement technique and its application to the analysis of materials behaviour under plane strain mode

The purpose of the paper is to provide a comprehensive experimental and numerical analysis of one of the encountered and critical state modes in sheet metal forming processes. The study is carried out with the help of the full-field measurement techniques. In order to confer some generality to the proposed work, several materials and different specimen shapes are considered that exhibit more or less homogeneous strain field. The proposed experimental study of the plane strain test is completed by a preliminary identification of the material parameters for non-linear behaviour at finite strains, using heterogeneous strain field.     

Stress–strain curves of metallic materials and post‐necking strain hardening characterization: A review

For metallic materials, standard uniaxial tensile tests with round bar specimens or flat specimens only provide accurate equivalent stress–strain curve before diffuse necking. However, for numerical modelling of problems where very large strains occur, such as plastic forming and ductile damage and fracture, understanding the post‐necking strain hardening behaviour is necessary. Also, welding is a highly complex metallurgical process, and therefore, weldments are susceptible to material discontinuities, flaws, and residual stresses. It becomes even more important to characterize the equivalent stress–strain curve in large strains of each material zone in weldments properly for structural integrity assessment. The aim of this paper is to provide a state‐of‐the‐art review on quasi‐static standard tensile test for stress–strain curves measurement of metallic materials. Meanwhile, methods available in literature for characterization of the equivalent stress–strain curve in the post‐necking regime are introduced. Novel methods with axisymmetric notched round bar specimens for accurately capturing the equivalent stress–strain curve of each material zone in weldment are presented as well. Advantages and limitations of these methods are briefly discussed.     

A 3D full‐field study of cracks in a nuclear graphite under mode I and mode II cyclic dwell loading conditions

Three‐dimensional (3D) full‐field deformation around crack tips in a nuclear graphite has been studied under mode I and mode II cyclic dwell loading conditions using digital volume correlation (DVC) and integrated finite element (FE) analysis. A cracked Brazilian disk specimen of Gilsocarbon graphite was tested at selected loading angles to achieve mode I and mode II cyclic dwell loading conditions. Integrated FE analysis was carried out with the 3D displacement fields measured by DVC injected into the FE model, from which the crack driving force J‐integral was obtained using a damaged plasticity material model. The evolution of near‐tip strains and the J‐integral during the cyclic dwell loading was examined. Under cyclic dwell, residual strain accumulation was observed for the first time. The results shed some light on the effect of dwell time on the 3D crack deformation and crack driving force in Gilsocarbon under cyclic mode I and II loading conditions.     

Plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant materials

The plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant material are investigated in this paper. Applying the stress-strain relation for the pressure-sensitive dilatant material, we have obtained an exact asymptotic solution for the plane strain tip fields for two types of cracks, one of which lies in the pressure-sensitive dilatant material and the other in the elastic material and their tips touch both the bimaterial interface. In cases, numerical results show that the singularity and the angular variations of the fields obtained depend on the material hardening exponent n, the pressure sensitivity parameter μ and geometrical parameter λ. This revised version was published online in August 2006 with corrections to the Cover Date.     

Factors affecting the reliability of precision measurement of liquid helium temperature in a dynamic regulation and stabilization mode

A study has been made of anomalies detected during precision measurements of liquid helium temperature, using secondary thermometers in a dynamic mode. An explanation is suggested for the physical nature of these anomalies.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 5, pp. 817–824, November, 1989.     

A finite element analysis of plane strain dynamic crack growth at a ductile-brittle interface

In this work, steady, dynamic crack growth under plane strain, small-scale yielding conditions along a ductile-brittle interface is analysed using a finite element procedure. The ductile solid is taken to obey the J ₂ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behaviour. The objectives of this work are to establish the validity of an asymptotic solution for this problem which has been derived recently [12], and to examine the effect of changing the remote (elastic) mode-mixity on the near-tip fields. Also, the influence of crack speed on the stress fields and crack opening profiles near the propagating interface crack tip is assessed for various bi-material combinations. Finally, theoretical predictions are made for the variation of the dynamic fracture toughness with crack speed for crack growth under a predominantly tensile mode along ductile-brittle interfaces. Attention is focused on the effect of mismatch in stiffness and density of the constituent phases on the above aspects.     

一种转角动柔度间接测量技术及在实验模态综合法中应用

将谐波集中力矩等效为谐波集中力系,用转角数值微分公式构造一种全新的转角动柔度间接测量技术,克服实验模态综合法中转角难测量与集中力矩难加载的困难。该间接测量技术无需附加任何质量块与施加集中力矩及集中力系,只需几次锤击实验或扫频实验,即可将集中力矩作用下的转角动柔度用集中力作用下的平动动柔度线性表示。将转角动柔度的间接测量技术应用于基于定频剩余动柔度的实验模态综合法中,数值实验表明,该转角动柔度间接测量技术切实可行,能有效解决实验模态综合法中界面自由度不匹配问题,可提高实验模态综合法精度及可靠性。