Modeling Stiffness Degradation of Fiber-Reinforced Polymers Based on Crack Densities Observed in Off-Axis Plies

A model that predicts the stiffness degradation in multidirectional reinforced laminates due to off-axis matrix cracks is proposed and evaluated using data from fatigue experiments. Off-axis cracks are detected in images from the fatigue tests with automated crack detection to compute the crack density of the off-axis cracks which is used as the damage parameter for the degradation model. The purpose of this study is to test the effect of off-axis cracks on laminate stiffness for different laminate configurations. The hypothesis is that off-axis cracks have the same effect on the stiffness of a ply regardless of the acting stress components as long as the transverse stress is positive. This hypothesis proves to be wrong. The model is able to predict the stiffness degradation well for laminates with a ply orientation similar to the one used for calibration but deviates for plies with different in-plane shear stress. This behavior can be explained by the theory that off-axis cracks develop by two different micro damage modes depending on the level of in-plane shear stress. It is found that besides influencing the initiation and growth of off-axis cracks, the stiffness degradation is also mode dependent.

Numerical Study of the Effect of Thixotropy on Extrudate Swell

The extrusion of highly filled elastomers is widely used in the automotive industry. In this paper, we numerically study the effect of thixotropy on 2D planar extrudate swell for constant and fluctuating flow rates, as well as the effect of thixotropy on the swell behavior of a 3D rectangular extrudate for a constant flowrate. To this end, we used the Finite Element Method. The state of the network structure in the material is described using a kinetic equation for a structure parameter. Rate and stress-controlled models for this kinetic equation are compared. The effect of thixotropy on extrudate swell is studied by varying the damage and recovery parameters in these models. It was found that thixotropy in general decreases extrudate swell. The stress-controlled approach always predicts a larger swell ratio compared to the rate-controlled approach for the Weissenberg numbers studied in this work. When the damage parameter in the models is increased, a less viscous fluid layer appears near the die wall, which decreases the swell ratio to a value lower than the Newtonian swell ratio. Upon further increasing the damage parameter, the high viscosity core layer becomes very small, leading to an increase in the swell ratio compared to smaller damage parameters, approaching the Newtonian value. The existence of a low-viscosity outer layer and a high-viscosity core in the die have a pronounced effect on the swell ratio for thixotropic fluids.

Rock Damage and Aquifer Property Estimation from Water Level Fluctuations in Wells Induced by Seismic Waves: A Case Study in X10 Well, Xinjiang, China

There is a coupling relationship between surrounding rock stress, deformation, and fracture evolution, especially in the microdynamics of the crust caused by mining activities and earthquakes. Previous research has investigated many cases regarding the coseismal water level responses and proposed a method to calculate the aquifer parameters by tidal analysis. However, to date, measurement of the degree of rock damage in the field has not been reported. Quantifying the fracture characteristics is essential for accurate evaluation of rock stability. This study has analyzed the relationship between the seismograms and hydroseismograms in response to the Mw 7.8 Solomon Islands earthquake and the Mw 7.8 Kaikōura earthquake, both events occurring in 2016. The calculated and measured changes in water level in the X10 well were fitted in order to study the relationships among the volumetric strain, the deviatoric strain, and the oscillations in the pore pressure. Then, we further estimate the degree of rock damage and the hydraulic characteristics of the aquifer. The results showed that the values for the rock damage parameter, 0.662 < αD < 0.754, and the Skempton coefficient, −0.100 < A < 0.026, estimated for the Solomon Islands earthquake signified higher damage and dilatancy in the X10 well. Also, the respective values for the parameters, 0.293 < αD < 0.363 and 0.226 < A < 0.251, calculated for the Kaikōura earthquake signified a lower degree of rock damage. It is concluded that the changes in the pore pressure were influenced by both the volumetric strain and the deviatoric strain. The degree of rock damage and the hydraulic properties of the aquifer estimated from the water level fluctuations in the wells which were induced by the seismic waves represent the actual aquifer characteristics.

A Thermodynamically Consistent Model of Quasibrittle Elastic Damaged Materials Based on a Novel Helmholtz Potential and Dissipation Function

In the paper, a thermodynamically consistent model of elastic damaged material in the framework of small strain theory is formulated, describing the process of deterioration in quasibrittle materials, concrete in particular. The main goal is to appropriately depict the distinction between material responses in tension and compression. A novel Helmholtz energy and a dissipation potential including three damage parameters are introduced. The Helmholtz function has a continuous first derivative with respect to strain tensor. Based on the assumed functions, the strain–stress relationship, the damage condition, the evolution laws, and the tangent stiffness tensor are derived. The model’s predictions for uniaxial tension, uniaxial compression, uniaxial cyclic compression–tension, and pure shear tests are calculated using Wolfram Mathematica in order to identify the main features of the model and to grasp the physical meaning of an isotropic damage parameter, a tensile damage parameter, and a compressive damage parameter. Their values can be directly bound to changes of secant stiffness and generalized Poisson’s ratio. An interpretation of damage parameters in association with three mechanisms of damage is given. The considered dissipation potential allows a flexible choice of a damage condition. The influence of material parameters included in dissipation function on damage mode interaction is discussed.

Equivalent Analysis of Thermo-Dynamic Blow-Off Impulse under X-ray Irradiation

X-ray thermodynamic effect is an important damage mode for spacecraft. Blow-off impulse as the main thermodynamic damage parameter has been widely studied by combining laboratory and numerical simulations. In this paper, most calculations and analyses have been carried out by using the self-developed software RAMA, including the equivalent calculation of blow-off impulse of monoenergetic and blackbody X-ray, and soft/hard blackbody X-ray irradiated at different incidence angles of LY-12 aluminium target. The results show that the characteristic mono-energetic X-ray can be exploited to simulate the blow-off impulse of the blackbody X-ray under certain conditions as a feasible equivalent method for the equal-flux and equal-impulse relations between mono-energetic and intense pulse blackbody of blow-off impulse. Moreover, the equivalent thermodynamic effect can be achieved between the point source radiation and parallel X-ray of X-ray. Furthermore, the cosine distribution of blow-off impulse is conducive to designing and calculating X-ray radiation load of hard aluminium corresponding to 1–5 keV blackbody spectrum. The mentioned results can be referenced for pulse X-ray simulation source and enhance the fidelity of the thermal-mechanical effect by electron beam. It is noteworthy that the study on the thermodynamic effects of intense pulsed X-ray is of high significance.

Evaluation of damage within sandwich honeycomb panels subjected to impact fatigue loading

This work was aimed at investigating damage evolution within sandwich panels consisting of aluminum skins and Nomex™ honeycomb core, with three different values of the core densities, subjected to multiple impacts. Repeated impacts at low energy were conducted using an impact fatigue machine. Bending tests were conducted to determine the residual stiffness after impacts in order to analyze the evolution of a damage parameter D. A model was therefore proposed for describing the changes in this parameter as a function of impact cycles N. After repeated impacts, the D(N) curves are characterized by an S-shaped curve. A good agreement is observed between model and experimental results, the maximum standard deviation being less than 7% for different densities. Microscopic observations of the impacted specimens were conducted in order to evaluate the crater growth (associated with permanent indentation). The influence of the number of impacts on the dimensions of the impact zone has also been evaluated. For all the core densities, the permanent indentation gradually increases as a function of impact cycles.

Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

Field and Numerical Study on Deformation and Failure Characteristics of Deep High-Stress Main Roadway in Dongpang Coal Mine

Deep horizontal high stress and high permeability geological factors appear when coal mines are converted to deep horizontal mining. When the roadway is damaged by the mining face, and the supporting components are mismatched, the deep roadways necessitate extensive repair work, which has a negative impact on the coal mining economy and sustainability. This paper carried out a series of field tests on the roadways deformation, crack distribution, and loose rock zone of the deep roadways. Furthermore, a numerical calculation model was established using the discrete element method (DEM) and calibrated with laboratory tests and RQD methods. Both the stress and crack distribution in the surrounding rock of the deep roadway were simulated. The field test and the corrected numerical model showed consistency. A FISH function was used to document the propagation of shear and tensile cracks around the roadway in three periods, and a damage parameter was adopted to evaluate the failure mechanism of the deep roadways under the dynamic stress disturbance. The matching of specifications of anchor cables, rock bolts, and anchoring agent is the primary point in the control of deep roadways, and revealing the stress evolution, crack propagation, and damage distribution caused by mining effects is another key point in deep roadway controlling. The field test and DEM in this paper provide a reference for the design of surrounding rock control of deep roadways and the sustainable development of coal mines.