Large Ductile Deformation Research Articles

How the Earth’s upper crust deforms in a viscous or brittle manner and how these behaviors interact and evolve over time: the crucial role of pressure solution creep and sealing processes1

Observations of the geological deformation of the Earth’s upper crust show both brittle behavior (faults) and viscous behavior (folds, shear zones). This paper explains the crucial role of pressure solution creep and sealing processes in these contrasting behaviors and in their evolutions over time. A description of natural deformation by pressure solution shows that the pressure solution creep process can accommodate large ductile deformation without any faults. This process can also accommodate near-stable ductile deformation through the coupling of pressure solution and fracturing. Even if pressure solution creep cannot accommodate the tectonic loading rate and earthquakes consequently occur, the post-seismic evolution is largely controlled by pressure solution processes such as post-seismic creep and fault healing and sealing. Some key experiments are presented that allow evaluating the thermodynamics and kinetics of these processes. Various models are then presented that could help engineers integrate pressure solution creep and sealing processes into predictions of the long-term behavior of rock deformation in underground storage and geo-energy facilities.

A novel genetic expression programming assisted calibration strategy for discrete element models of composite joints with ductile adhesives

Discrete element (DE) model has a great feasibility in modelling the microstructural behaviours of adhesive composite joints. However, it demands a sophisticated calibration process to determine microscale bond parameters, which involves massive efforts in both experimental and numerical investigations. This work developed a novel calibration strategy based on DE models and genetic expression programming (GEP) approach for predicting the behaviours of hybrid composite joints encompassing the material nonlinearity, large ductile deformation and multiple fracture modes. In the developed strategy, both the bulk and interlaminar-like properties of ductile adhesives were concerned to suit various joint configurations. GEP modelling was performed based on the datasets from virtual DE experiments. Symbolic regression models were subsequently developed to facilitate the parameters determination. A series lab tests were conducted to validate the numerical results. It shows that the calibrated DE model can adaptively simulate the featured behaviours of both the ductile adhesive and composite joints with different configurations well in most examined occasions. Therefore, it could be suggested to generalize the developed strategy in the development of other DE models for saving the massive efforts in the calibration process of microstructural parameters.

Deformation and failure modes of aluminum foam-cored sandwich plates under air-blast loading

In this paper, air-blast experiments were firstly carried out to investigate the deformation and failure modes of aluminum foam-cored sandwich plates. The maximum midpoint deflection of the foam-cored sandwich plates was assessed by using a 3D scanning device considering the effects of different impulses. Failure modes of each components were analyzed. Based on that, a finite element model was proposed to verify the experimental results and to gain a further understanding of the air-blast process. It was found that: (1) there was a positive correlation between the maximum midpoint deflection of the rear plate and the revised dimensionless impulses; (2) the effects of the quasi-static air pressure should be taken into account in the short-distance blast resistance structural design; (3) the major failure modes of the core layer included large overall deformation, local compression, fragmentation and fly-out; (4) the failure modes of the face sheets mainly presented as large ductile deformation and petalling. (5) The energy absorption was mainly dominated by the foamed-core part.

Dynamic Response of Copper Plates Subjected to Underwater Impulsive Loading

Understanding the mechanical response and failure behaviors of thin plates under impact loading is helpful for the design and improvement of thin plate structures in practical applications. The response of a copper plate subjected to underwater impulsive loading has been studied in fluid-structure interaction (FSI) experiments. Three typical copper plates, (a) without a pre-notch, (b) with a cross-shaped pre-notch (+), and (c) with a ring-shaped pre-notch (○) were selected. A high-speed photography system recorded the full-field shape and displacement profiles of the specimens in real time. The 3D transient deformation fields’ measurements were obtained using a 3D digital image correlation (DIC) technique. Strain results from DIC and the strain gauges technique were in good agreement. A dimensionless deflection was used to analyze the effect of plate thickness and loading intensity on the deformation of the copper plates. The typical failure modes of different copper plates were identified. The test plates exhibited large ductile deformation (mode I ) for copper plates without a pre-notch, and large ductile deformation with local necking (mode I c ), splitting (mode II ), splitting and tearing (mode II c ), and fragment (mode III ) for the copper plate with a pre-notch.

Mechanical properties of microconstituents in Nb-Si-Ti alloy by micropillar compression and nanoindentation

The micromechanical properties of both Nb solid solution (Nbss) and (Nb,Ti)3Si silicide in a ternary Nb-16Si-22Ti (in at%) alloy were evaluated by nanoindentation and micropillar compression techniques. Nanoindentation tests showed that (Nb,Ti)3Si possesses much higher hardness (15.6±0.6GPa) and Young's modulus (253.3±8.4GPa) than Nbss (5.2±0.4GPa and 124.9±5.1GPa, respectively). Stress-strain curves of each constituent were obtained by micropillar compression. The stress-strain behavior showed that (Nb,Ti)3Si exhibited a brittle fracture mode, while Nbss was able to bear large ductile deformation. The compressive failure strength of (Nb,Ti)3Si intermetallic and yield strength of Nbss were found to be 8.4±1.2GPa and 0.9±0.1GPa, respectively. The fracture toughness of the (Nb,Ti)3Si phase evaluated by cracks emanating from nanoindentation, was measured to be ~2.3MPa-m1/2.

Impact Loading of Ductile Rectangular Plates

Abstract In many industries, rigid-plastic methods of analysis are a useful design aid for safety calculations, hazard assessments, security studies and forensic investigations of ductile structures, which are subjected to large dynamic loads producing an inelastic response. This paper examines the behaviour of a rectangular plate struck at the centre by a rigid mass impact loading. A theoretical method has been developed previously for arbitrarily shaped plates which retains the influence of finite transverse displacements, or geometry changes. It is used in this paper to predict the maximum permanent transverse displacements and response duration of plates having boundary conditions characterised by a resisting moment mM 0 around the entire boundary, where m =0 and 1 give the two extreme cases of simply supported and fully clamped supports, respectively. The theoretical predictions are compared with some experimental data recorded on fully clamped metal rectangular plates having a range of aspect ratios and struck by masses travelling with low impact velocities up to nearly 7 m/s and which produce large ductile deformations without failure. The theoretical analysis gives reasonable agreement with the corresponding experimental data for masses having blunt, conical and hemispherical impact faces. For sufficiently large initial impact energies, the projectile would perforate a plate and, for completeness, a useful design equation is presented which predicts perforation energies larger than all of the test data, as expected.

Fracture behaviour of polycrystalline tungsten

Fracture behaviour of round blank polycrystalline tungsten was studied by means of three point bending Fracture-Mechanical (FM) tests at temperatures between RT and 1000°C and under high vacuum. To study the influence of the anisotropic microstructure on the fracture toughness (FT) and ductile-to-brittle transition (DBT) the specimens were extracted in three different, i.e. longitudinal, radial and circumferential orientations. The FM tests yielded distinctive fracture behaviour for each specimen orientation. The crack propagation was predominantly intergranular for longitudinal orientation up to 600°C, whereas transgranular cleavage was observed at low test temperatures for radial and circumferentially oriented specimens. At intermediate test temperatures the change of the fracture mode took place for radial and circumferential orientations. Above 800°C all three specimen types showed large ductile deformation without noticeable crack advancement. For longitudinal specimens the influence of the loading rate on the FT and DBT was studied in the loading rate range between 0.06 and 18MPam1/2/s. Though an increase of the FT was observed for the lowest loading rate, no resolvable dependence of the DBT on the loading rate was found partly due to loss of FT validity. A Master Curve approach is proposed to describe FT vs. test temperature data on polycrystalline tungsten. Fracture safe design space was identified by analysis compiled FT data.

Impact loading of ductile rectangular plates

In many industries, rigid-plastic methods of analysis are a useful design aid for safety calculations, hazard assessments, security studies and forensic investigations of ductile structures, which are subjected to large dynamic loads producing an inelastic response. This paper examines the behaviour of a rectangular plate struck at the centre by a rigid mass impact loading. A theoretical method has been developed previously for arbitrarily shaped plates which retains the influence of finite transverse displacements, or geometry changes. It is used in this paper to predict the maximum permanent transverse displacements and response duration of plates having boundary conditions characterised by a resisting moment mM 0 around the entire boundary, where m=0 and 1 give the two extreme cases of simply supported and fully clamped supports, respectively. The theoretical predictions are compared with some experimental data recorded on fully clamped metal rectangular plates having a range of aspect ratios and struck by masses travelling with low impact velocities up to nearly 7 m/s and which produce large ductile deformations without failure. The theoretical analysis gives reasonable agreement with the corresponding experimental data for masses having blunt, conical and hemispherical impact faces. For sufficiently large initial impact energies, the projectile would perforate a plate and, for completeness, a useful design equation is presented which predicts perforation energies larger than all of the test data, as expected.

On the Scaling of Low-Velocity Perforation of Mild Steel Plates

Experimental results are reported for the perforation of geometrically similar fully clamped circular and square mild steel plates struck transversely by cylindrical projectiles having blunt, conical, and hemispherical noses. The striking masses are much heavier than the corresponding plate mass and travel with initial impact velocities up to about 12m∕s. The blunt projectiles perforate the plating easiest, while the hemispherical-nosed ones require the greatest energy. The perforation energy of a conical-nosed projectile is somewhat less than that for a hemispherical-nosed one. The data are used to explore the validity of the geometrically similar scaling laws over a geometric scale range of 4. The experimental results are compared to the empirical equations for the impact perforation of plates and with theoretical rigid-plastic predictions for the large ductile deformation behavior of those test specimens, which did not suffer cracking or perforation. The experimental results satisfy the requirements of geometrically similar scaling and some simple equations are presented, which are useful for design purposes.

The deformation and shear failure of peripherally clamped centrally supported blast loaded circular plates

An experimental investigation of deformation and shear failure in peripherally clamped centrally supported (PCCS) blast loaded circular plates is presented. In particular, the timing of shear failure events and the associated magnitude of the shear forces are reported. The plates exhibited three distinct modes of failure: mode I (large ductile deformation), mode II (boundary failure after large deformation) and mode III (boundary failure prior to large deformation). Approximate energy analyses for mode I deformation of annular and PCCS plates are presented. An expression for dimensionless impulse, applicable to annular and PCCS plates, is derived. The experimental data and analytical predictions exhibit satisfactory correlation.

The numerical modelling of ceramics subject to impact using adaptive discrete element techniques

In recent years, developments in the field of lightweight armour have been of primary importance to the defence industry. This necessity has led to many organisations adopting composite armours comprising both the traditional heavy armours and new lighter weight ceramic armours. The numerical modelling of metal based armour systems has been well documented over the years using purely continuum based methods; and also the modelling of brittle systems using discrete element methods, therefore it is the objective of this paper to demonstrate how a coupled finite and discrete element approach, can be used in the further understanding of the quantitative response of ceramic systems when subjected to dynamic loadings using a combination of adaptive continuum techniques and discrete element methods. For the class of problems encountered within the defence industry, numerical modelling has suffered from one principal weakness; for many applications the associated deformed finite element mesh can no longer provide an accurate description of the deformed material, whether this is due to large ductile deformation, or for the case of brittle materials, degradation into multiple bodies. Subsequently, two very different approaches have been developed to combat such deficiencies, namely the use of adaptive remeshing for the ductile type materials and a discrete fracture insertion scheme for the modelling of material degradation. Therefore, one of the primary objectives of this paper is to present examples demonstrating the potential benefits of explicitly coupling adaptive remeshing methods to the technique of discrete fracture insertion in order to provide an adaptive discontinuous solution strategy, which is computationally robust and efficient.

Low-temperature deformation mechanisms at a lithotectonic interface near the Sudbury Basin, Eastern Penokean Orogen, Canada

Southwest of the Sudbury Basin, variations in macroscopic strain, microstructure and deformation mechanisms within Archaean granitoid basement and overlying Proterozoic rocks suggest that rock strength was strongly influenced by large amounts of fluids. Ductilely deformed granitoids with strong shape fabrics are concentrated in a 150–200-m-wide zone parallel to the subvertical basement-cover interface. High fluid activity in this zone is indicated by: (1) thickness and close spacing of foliation-parallel quartz veins, (2) abundant fluid-inclusion trails in quartz; (3) quartz c-axis fabrics: and (4) transformation of feldspar into phyllosilicates under middle greenschist-facies metamorphic conditions. Away from this zone, brittle-ductile deformation in Archaean granitoids caused grain size reduction of feldspar by fracturing and crystal-plastic deformation of quartz indicating largely ‘dry’ conditions. Strain was concentrated at the interface, in a region of bulk horizontal shortening and linked kinematically to large-scale shortening of the Sudbury Igneous Complex and thrusting in the South Range Shear Zone. After early open buckling of the Sudbury Igneous Complex, reverse shearing in this zone may have been controlled by ductile deformation at the basement-cover interface. Physical continuity of, and age constraints on, strain fabrics suggest that the South Range Shear Zone represents a segment of a large ductile deformation zone which is most likely linked to the Murray fault and on which higher-grade rocks ascended between 1.85 and 1.23 Ga ago.

A Study on the Large Ductile Deformations and Perforation of Mild Steel Plates Struck by a Mass—Part I: Experimental Results

An experimental study is reported on the ductile deformation and perforation of plates struck at the center by solid cylindrical projectiles having the longitudinal axis normal to the plate surface. The plates, which are made from 4 to 8-mm-thick mild steel sheet, are fully clamped around a circular boundary and are struck by projectiles having blunt ends and traveling with impact velocities within the range 7.7–118.9 m/s. Comparisons are made in Part II with the static perforation behavior and with previously published experimental results and several empirical equations for the impact case. A new empirical equation, which retains the influence of the impact velocity on the perforation energy, is also proposed in Part II.

A Study on the Large Ductile Deformations and Perforation of Mild Steel Plates Struck by a Mass—Part II: Discussion

An experimental study into the ductile deformations and static and impact perforation of mild steel plates is reported in Part I. These results are discussed in this article and compared with other experimental data reported in the literature. The accuracy of various empirical formulas for the impact perforation of plates is also examined.

The deformation and tearing of thin square plates subjected to impulsive loads—An experimental study

Experimental results for clamped mild steel square plates subjected to impulsive loads are reported. The strain rate-sensitive plates exhibit mode I (large ductile deformation), mode II (tensile-tearing and deformation) and mode III (transverse shear) failure modes. Three phases of mode II are identified as mode II ∗ (partial tearing), mode IIa (complete tearing with increasing mid-point deformation), and mode IIb (complete tearing with decreasing mid-point deformation). For the cases where complete tearing occurs (modes II and III) the velocity of the square disc torn from the base plate is measured. An attempt to measure the speed of rotation of the disc is discussed. Threshold for the onset of failure modes II and III are given. Comparisons between the response of square and circular plates are discussed.

Deformation and tearing of blast-loaded stiffened square plates

Experimental and numerical results for fully built-in stiffened square plates subjected to blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation) and mode II (tensile tearing) failure as the load intensity increases. The numerical analysis is carried out using a finite element formulation which incorporates non-linear geometry and material effects as well as strain rate sensitivity. Mode I is predicted well for both maximum deflection and deformation shape. Initiation of mode II failure is predicted by a maximum strain criterion, but the limited mode II data is insufficient for conformation.

Metallurgical Investigation of HSLA Steel Subjected to Underwater Explosion

The metallurgical behaviour of HSLA steel subjected to underwater explosion is of prime importance because of its structural applications in underwater vehicles. HSLA steel plates 300 × 250 × 4 mm were subjected to single and repetitive shock loadings and the point of rupture was identified. Test plates exhibited mode-I (large ductile deformation) and mode-II (tensile tearing) macroscopic failures. Electron micrographic and fractographic examination showed that the initiation of fracture was due to adiabatic shearing and the microscopic mode of failure was ductile. Plates subjected to single shock showed an increase in residual hardness and at the point of rupture it was approximately one-third higher than the initial residual hardness.

Metallurgical Investigation of HSLA Steel Subjected to Underwater Explosion

The metallurgical behaviour of HSLA steel subjected to underwater explosion is of prime importance because of its structural applications in underwater vehicles. HSLA steel plates 300 × 250 × 4 mm were subjected to single and repetitive shock loadings and the point of rupture was identified. Test plates exhibited mode-I (large ductile deformation) and mode-II (tensile tearing) macroscopic failures. Electron micrographic and fractographic examination showed that the initiation of fracture was due to adiabatic shearing and the microscopic mode of failure was ductile. Plates subjected to single shock showed an increase in residual hardness and at the point of rupture it was approximately one-third higher than the initial residual hardness.

Deformation and rupture of blast loaded square plates—predictions and experiments

Experimental and numerical results for clamped square mild steel plates subjected to uniformly distributed blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation), mode II (tensile-tearing), and a trend towards mode III (transverse shear) failure as the load intensity increases. The numerical analysis is carried out using a new finite element formulation which incorporates nonlinear geometry and material effects as well as strain rate sensitivity. Initiation of mode II failure is predicted by a maximum strain criterion. Mode I is predicted well for both maximum deflection and deformation shape. The mode II failure prediction correlates reasonably well with the experimental results and provides a clear lower bound for full rupture of the plate.

The deformation and tearing of thin circular plates subjected to impulsive loads

This investigation examines the failure of circular plates subjected to impulsive velocities. Experiments are conducted on fully clamped circular mild steel plates subjected to a uniformly distributed impulse. The strain rate-sensitive plates exhibit mode I (large ductile deformation), modes II (tensile-tearing and deformation) and mode III (transverse shear) failure modes. An energy analysis is used on the test results which enables an energy balance equation relating input, deformation, tearing and disc energies to be formulated. The input and disc energies are obtained from experimental measurements; the deformation energy is predicted by making use of the final deformed height, a shape function and a rigid-plastic analysis. Good correlation is found and the experiments show good repeatability. The threshold velocities for the onset of failure modes II and III are given.