Linear Elastic Strain Energy Research Articles

Energy-Based Fatigue Assessment of Defect-Afflicted Cast Steel Components by Means of a Linear-Elastic Approach

Cast steel components are affected by manufacturing process-based imperfections, which severely limit their fatigue strength. In this work, the linear-elastic strain energy density concept is applied to assess the fatigue behaviour of bulk defect-afflicted components made of high-strength cast steel alloy G12MnMo7-4+QT. Based on analytical calculations, an energy-based design limit curve is derived which merges experimental results of notched and unnotched small–scale specimens into a statistically proven scatter band. The stress ratio dependency is also investigated. Moreover, a numerical methodology is introduced, which facilitates the energy-based fatigue assessment of complex spatial imperfections on the basis of radiographs. Validation of the established framework utilizing experimental results of defect-afflicted large–scale specimens leads to sound accordance of numerically and experimentally derived fatigue strength values, showing an average deviation of about only eight percent.

Discussions on the Complete Strain Energy Characteristics of Deep Granite and Assessment of Rockburst Tendency

In deep mining, the rockburst hazard has become a prominent problem. Rockburst is difficult to be predicted, and it gives a severe threat to mining safety. In this paper, the triaxial compressive tests with an acoustic emission (AE) device and full cyclic loading and unloading tests were carried out, respectively, to present characteristics of linear elastic strain energy and peak strain energy. Also, to consider the time-delay strain characteristics of granite found in the abovementioned tests, a new stage loading and unloading test with dual monitoring systems was designed and performed. Through 20 days’ time-delay strain monitoring, the peak-strength strain energy was further modified. The results showed that the peak strain energy is approximate 1.2-1.3 times than linear elastic strain energy under the same confining pressure, and after considering the time-delay strain effect, the modified maximal strain energy value of the deep granite significantly increased. The peak strain energy values are further enhanced from 1.0 × 104 J/m3 to 1.8 × 104 J/m3, respectively. At last, by taking advantage of the strain energy index model of rockburst, the tendency and intensity of rockburst were assessed contrastively.

A micro-potential based Peridynamic method for deformation and fracturing in solids: A two-dimensional formulation

A two-dimensional micro-potential based Peridynamic (MPPD) formulation is proposed to investigate deformation and fracturing in solid materials. To this end, square measure of the bond length change is applied and a generalized Peridynamic (PD) strain for plane stress and strain problems is developed to decompose the bond length change into two parts, one resulting from the volumetric PD strain and the other from the deviatoric PD strain. The micro-potential generated in the deformed bond is postulated as a function of both length change components. The nonlocal elastic strain energy density (NESED) at a material point is computed by the integral of the bond potential over the horizon. Through the Frechet derivative of the NESED, a general constitutive relation depending on the micro-potential function is well formulated. The model parameters are calibrated through the equivalence of the NESED with the linear elastic strain energy density. Several specific micro-potential functions and their corresponding constitutive force densities are carefully discussed. The discussions reveal that the proposed MPPD model not only can retrieve the well-known bond based PD model, but also allows specific materials with any Poisson ratio to be represented. Moreover, one failure criterion based on the total micro-bond potential is developed for the present model. The reliability and efficiency of the MPPD model is demonstrated through numerical tests. Simulation results show that the proposed model is capable of investigating deformation and cracking in solids.

Fracability evaluation of lacustrine shale by integrating brittleness and fracture toughness

Rock brittleness and fracture toughness are important parameters for evaluating rock fracability. The stress-strain curves indicate that the lacustrine shale is strongly brittle. Brittle failure occurs rapidly when the stress of the lacustrine shale reaches its peak value. In addition, the lacustrine shale has different plastic strains before and after peak stress; this can relax the stress concentration of the crack tips. Therefore, the plastic strain that occurs before and after the peak stress can cause decreasing brittleness, which can be used to distinguish the brittleness and fracability in the formation of the lacustrine shale clearly. Moreover, this further enlarges the difference in the brittleness index. Based on the influence of plastic strain on brittleness, we have developed a new brittleness evaluation method that uses the ratio of linear elastic strain energy to the total strain energy before complete rock failure, which can indicate the difference of the lacustrine shale clearly. Fracture toughness is another important parameter that impacts the fracture extension and influences fracability. Based on the impact of brittleness and fracture toughness on the fracability, we have developed a new fracability evaluation method. The brittleness index increases with increases in the quartz content, and it decreases with increases in the albite feldspar and calcite contents. The fracture toughness decreases with increases in the quartz and clay contents, and it increases with increases in the siderite content. In addition, we established an empirical formula that can evaluate the brittleness index and the fracture toughness using mineral contents obtained from elemental logging. Using the new fracability evaluation method to optimize the fracturing stage, the preliminary field test indicates that the new approach was effective in the lacustrine shale formation.

Correlation among Energy Based Fatigue Curves and Fatigue Design Approaches

In this paper, with reference to the strain controlled fatigue characterization of AISI 304L stainless steel, the correlations between plain material fatigue curves based on different definitions of the strain energy densities, namely the elastic, plastic and elastoplastic strain energy densities evaluated under the cyclic stress-strain curve and the plastic strain hysteresis energy density (per cycle and total at fracture) are investigated. On this basis, a diagram showing the link among the different energy-based fatigue curves is proposed and is applied to find the correlation between plain material strain energy density fatigue curves and some fatigue strength assessment methods for notched structural components, namely the one based on the experimental evaluation of the heat energy dissipated by the material per cycle and the one based on the evaluation of the linear elastic strain energy density, averaged in a properly defined structural volume.

Strain energy-and stress-based approaches revisited in notch fatigue of ductile steels

The constant amplitude, zero-mean stress, axial-fatigue behaviour of plain and bluntly notched AISI 304 L stainless steel specimens is investigated in terms of strain energy density. Concerning plain material, it was found that at the fatigue knee the plastic strain energy density is 1.49 times higher than the elastic strain energy density. In the authors’ opinion, the presence of plasticity at the fatigue knee is responsible for the unsuitableness of classical stress - based approaches to synthesise the fatigue behaviour of this material. On the contrary, the elastic-plastic strain energy density was found an efficient parameter to rationalise in a single scatter band fatigue data of plain and bluntly notched specimens. Based on this result, the classic stress-and the point stress-based approaches were revisited taking into account the presence of plasticity at the fatigue knee, by introducing an equivalent fully elastic material having a linear elastic strain energy density at the fatigue knee equal to that of the actual material. Accordingly, a coefficient of plasticity Kp was successfully introduced to modify the classical definition of fatigue strength reduction factor, Kf.

Extension of linear elastic strain energy density approach to high temperature fatigue and a synthesis of Cu-Be alloy experimental tests

Article history: Received October 6, 2014 Accepted 28 January 2015 Available online 29 January 2015 The present paper summarizes the results from uniaxial-tension stress-controlled fatigue tests performed at different temperatures up to 650°C on Cu-Be specimens. Two geometries are considered: hourglass shaped and plates weakened by a central hole (Cu-Be alloy). The motivation of the present work is that, at the best of authors’ knowledge, only a limited number of papers on these alloys under high-temperature fatigue are available in the literature and no results deal with notched components. The Cu-Be specimens fatigue data are re-analyzed in terms of the mean value of the Strain Energy Density (SED) averaged over a control volume. Thanks to the SED approach it is possible to summarize in a single scatter-band all the fatigue data, independently of the specimen geometry. © 2015 Growing Science Ltd. All rights reserved.

High Temperature Fatigue Tests of a Cu-Be Alloy and Synthesis in Terms of Linear Elastic Strain Energy Density

The present paper summarises the results from uniaxial-tension stress-controlled fatigue tests performed at different temperatures up to 650°C on Cu-Be specimens. Two geometries are considered: hourglass shaped and plates weakened by a central hole (Cu-Be alloy). The motivation of the present work is that, at the best of authors’ knowledge, only a limited number of papers on these alloys under high-temperature fatigue are available in the literature and no results deal with notched components.The Cu-Be specimens fatigue data are re-analyzed in terms of the mean value of the Strain Energy Density (SED) averaged over a control volume. Thanks to the SED approach it is possible to summarise in a single scatter-band all the fatigue data, independently of the specimen geometry.

A comprehensive fatigue failure criterion based on thermodynamic approach

In this work, stress curve and energy-based (linear elastic strain energy, and hysteresis loop energy) fatigue failure criteria are compared with a new, entropy-based model for the prediction of fatigue life in a woven glass/epoxy laminate. Extensive experimental results are reported that involve load-controlled tension–tension fatigue test with two different stress ratios as well as constant- and variable-loading of a woven glass/epoxy laminate with various load angles. The plot of fracture fatigue entropy vs. fatigue life is compared with the energy plotted vs. number of cycle and stress plotted vs. number of cycle (i.e., the so-called S–N curve) plots.

Mechanics of Materials with Periodic Truss or Frame Micro-Structures

This paper describes the mechanics of materials with periodic skeletal micro-structures in infinite domains. The principal technical results consist of certain Korn-type inequalities that provide upper and lower bounds for the linear elastic strain energy in the material. Using these inequalities, existence and uniqueness results for the equations of linear elastic equilibrium are derived, and some asymptotic properties of the solutions are described. Particular attention is paid to the question of when a lattice structure can accurately be modeled as a pin-jointed truss, and when a rigid-node frame model must be employed. A practical technique for how to distinguish between the two types of material is given, and the distinct differences in their mechanical behavior are described.

Polymer/metal interfacial crack growth characterized by C*

This paper establishes a simple testing scheme to simultaneously measure the linear elastic strain energy release rate G, the non-linear J-integral, and the rate-dependent C*-integral for a growing crack at a polymer/metal interface. The test is applicable to fracture of adhesive bonds. A criterion governing C*-controlled fracturing is derived, analogous to the Hutchinson-Paris ω-criterion for J-controlled growth. The interfacial toughness of an adhesive commonly used for bonding metal plates is characterized at room temperature, and is shown to fracture in a C*-controlled manner. A relationship between C* and the crack growth rate is observed. The nature of this relationship warrants further exploration.

Modelling the effect of cracks on interlaminar shear strength

Short-beam shear tests of unidirectional carbon fibre/epoxy are analysed assuming shear deformations to be concentrated at the resin-rich interfacial layers between plies. A two-dimensional finite element model is used with linear elastic continuum elements to represent the plies, and non-linear springs to model the interfaces. This approach is shown to be satisfactory provided that there is a sufficiently large number of plies. The effect of cracks of varying length and at different positions is investigated. Linear elastic strain energy release rate analysis indicates that there is not sufficient energy for small cracks to propagate. In contrast, the non-linear interface modelling approach predicts that small cracks can have a significant effect on interlaminar shear strength. Excellent correlation is obtained with experimental data, and it shown that the presence of small defects is a plausible explanation for the scatter in results commonly observed in short-beam shear tests.

Fracture characterization of short glass fibre reinforced thermoplastic polyester by theJ-integral

Fracture initiation of short glass fibre reinforced thermoplastic polyester was characterized by theJ-integral measurement based on the energy release rate interpretation ofJ. The criticalJ value (Jc) is shown to be a fracture characterizing parameter for the onset of the crack initiation in the injection moulded short glass fibre reinforced composite material. TheJc value of the composite is estimated by be 6.0kJ m−2. This value is in good agreement with the linear elastic strain energy release rate (Gc), since the composite exhibited a fairly linear stress-strain relationship. The estimated ratios ofJc to the total energy absorbed per unit uncracked area are in good agreement with the analytically obtained values after the remote energy dissipation due to fibre and matrix interaction away from the crack tip has been subtracted from the total energy.