Variation Of Normal Stress Research Articles

Characterization of laboratory-scale hydraulic fracturing for EGS

To investigate the impact of reservoir stimulation by hydraulic fracturing, a series of advanced lab-scale block tests were conducted with multiple measurement methods to characterize the fracture and to assess the operation and the performance of an enhanced or engineered geothermal system (EGS). The stimulation test samples were 330-mm cubic blocks of Sierra White granite with one injection well and four producers drilled into it. Acoustic emissions generated during the fracture initiation and propagation were monitored with twenty AE sensors mounted on all sides of the block to help characterize the fracture initiation and propagation process. The recorded AE signals were analyzed to obtain the event location and the failure mechanism. The localized AE events shows that due to the low viscosity of the fracturing fluid (water), the fracture propagated rapidly and took only about 1.4 s to reach near the block surface. During the fracturing phase, about 47 percent of the events were determined to be shear/mixed mode failure events, 28 percent tensile failure events, and 25 percent compressional failure events. Just after the simulation, a step-rate (constant flowrate) injection test was carried out to investigate the reservoir injectivity enhancement. During this phase additional compressional failure events were observed and the percentages of tensile failure and shear/mixed mode failure decreased. The dramatic increase of the injection rate with small increments of the injection pressure demonstrates the nonlinear response of the fracture to effective normal stress variation with much higher fracture opening increase during the low effective normal stress interval. Hydraulic fracturing tests under different stress levels show that more AE hits/events are recorded when the rock block is under higher applied stress. The reconstructed 3D fracture geometry shows good agreement with the AE monitoring results. After fracturing, a tracer test was carried out and the fracture aperture was estimated to be around 139 μm. The tracer recovery curve shows two linear portions of the tracer tail on a semi-log plot similar to that observed in some field data and predicted by numerical modeling. Laser scanning of the fracture surfaces indicates that the induced fracture has a rough surface with a joint roughness coefficient (JRC) of 12.98 and tortuosity of 1.10, both of which are slightly larger than that from the Brazilian test fracture on the same rock. The thin section and SEM observations show that the fracture follows the weak boundaries between the Quartz and Albite grains or the weak beddings in the grains.

Semianalytical Geometry-Property Relationships for Some Generalized Classes of Pentamodelike Additively Manufactured Mechanical Metamaterials

We study a special class of mechanical metamaterials, namely lattices, based on beams (struts) with nonuniform cross sections, of which pentamode mechanical metamaterials are a special case. Five symmetric beam types including simple cylinder, concave double cone, convex double cone, concave hyperbolic, and convex hyperbolic are considered. Three types of loads including lateral force, axial force, and moment are applied to the free end of cantilever beams with the five aforementioned geometries and their responses are compared in terms of displacement, normal stress variation along the beam length, and shear stress variation along the beam length. Using the displacement diagrams obtained for different strut geometries and loading conditions, semi-analytical relationships are derived for the displacement at the end of cantilever beams. The semi-analytical relationships are then used to calculate the elastic modulus and yield strength of lattice structures based on two types of unit cells, namely diamond and cube. We also build numerical models and perform experiments to benchmark our semi-analytical results. Comparison of the analytical, numerical, and experimental results demonstrate the accuracy of the semi-analytical relationships presented for the mechanical properties of this class of mechanical metamaterials. Moreover, in both the cube- and diamond-based structures, increasing the α value (i.e., the ratio of the largest to the smallest cross-section radius in each strut) at a constant relative density decreases the elastic modulus, yield strength, the initial maximum stress, and the plateau stress.

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

AbstractEntropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (), viscosity variation parameter (), and viscous dissipation parameter (). Also, group parameter (), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of , , and Gr. The converse trend is noticed with increasing Pr and . Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall.

Static deflection and thermal stress analysis of non-uniformly heated tapered composite laminate plates with ply drop-off

The effective design of tapered laminated composite structures subject to non-uniform temperature fields requires a thorough understanding of their static behaviour. In this study, a finite element analysis of tapered laminated composite plates with ply drop-off has been carried out to study the static deflection and normal stress patterns developed under non-uniform heating. The study revealed that the nature of the taper configuration, the nature of the applied temperature field and the structural boundary conditions influence the static deflection behaviour and the normal stresses developed in the tapered composite plates. It is found that the static deflection pattern of a tapered plate subject to a particular temperature profile is not sensitive to the nature of the taper configuration. It is also observed that the static deflection pattern of a tapered plate is significantly influenced by the nature of temperature field. Normal stress variation of tapered plates subject to various temperature fields reflects the nature of the temperature profile. Maximum normal stress occurs at locations where the highest temperature exists for that particular temperature field. The stresses are also influenced by the nature of the taper - Taper D plates experience low stresses while Taper B and Taper C plates experience similar values. It was also found that large variations in stresses are observed at resin pockets.

An Analytical Model for Two-Order Asperity Degradation of Rock Joints Under Constant Normal Stiffness Conditions

Jointed rock masses during underground excavation are commonly located under the constant normal stiffness (CNS) condition. This paper presents an analytical formulation to predict the shear behaviour of rough rock joints under the CNS condition. The dilatancy and deterioration of two-order asperities are quantified by considering the variation of normal stress. We separately consider the dilation angles of waviness and unevenness, which decrease to zero as the normal stress approaches the transitional stress. The sinusoidal function naturally yields the decay of dilation angle as a function of relative normal stress. We assume that the magnitude of transitional stress is proportionate to the square root of asperity geometric area. The comparison between the analytical prediction and experimental data shows the reliability of the analytical model. All the parameters involved in the analytical model possess explicit physical meanings and are measurable from laboratory tests. The proposed model is potentially practicable for assessing the stability of underground structures at various field scales.

The effects of stress on reactions in the Earth: Sometimes rather mean, usually normal, always important

AbstractStress affects chemical processes on all scales in the Earth but the magnitude of its effect is debated. Here, I give a new synthesis of the theory that describes the effects of stress on chemistry, elaborating upon work in Materials Science which is built from fundamental thermodynamic laws, and show its significance in Earth Science. There are separate but compatible relationships describing what happens (1) at interfaces and (2) within grains. (1) The main chemical effects of stress in the Earth are due to variations in normal stress along grain interfaces and between interfaces with different orientations. For reactions involving diffusion these variations give effects on mineral stability broadly equivalent to pressure changes of (molar volume)/(molar volume change during reaction) × (stress variation). The volume ratio is generally large and so the effects of normal stress variations are always important since all stressed rocks have interfaces supporting different normal stresses. There is no global chemical equilibrium in a stressed system, so reaction kinetics contribute to ongoing evolution until stresses relax: this evolution can include deformation by diffusion creep and pressure solution, possibly with new mineral growth. These effects are relevant for predicting the conditions for reactions involving fluids, such as serpentinite formation and breakdown (relevant for the Earth's volatile cycles) and for other reactions such as ringwoodite breakdown (relevant for understanding the 660 km mantle discontinuity). (2) Within stressed solid solution grains it is not possible to define chemical potentials of all chemical components since one has to be specified as “immobile.” The chemical potential of a “mobile” component such as an exchange vector can be defined. It depends on the “partial molar strain,” a second rank tensor defining the variation in unit cell geometry with composition. In cubic crystals the partial molar strain is isotropic and the chemical potential of a mobile component depends on mean stress. In other crystal systems the partial molar strain is anisotropic and the chemical potential depends on a “weighted” mean stress; orientation as well as magnitude of stress has an influence. I propose “chemical palaeopiezometry”—the possibility of measuring past stress levels via chemistry. Examples show that stress variations in hundreds of MPa to GPa are required to produce 2% variations in composition but high stresses and/or precise chemical analyses will allow this proposal to be tested. High stresses around inclusions and dislocations could be targeted. So, the weighted mean stress inside grains has an effect which is relatively minor although potentially valuable in explaining chemical variations; the normal stress at interfaces plays the main role in chemical processes and its effects are of significant magnitude.

Segmentation of Slow Slip Events in South Central Alaska Possibly Controlled by a Subducted Oceanic Plateau

AbstractRecent GPS observations show that slow slip events in south central Alaska are segmented along strike. Here we review several mechanisms that might contribute to this segmentation and focus on two: along‐strike variation of slab geometry and effective normal stress. We then test them by running numerical simulations in the framework of rate‐and‐state friction with a nonplanar fault geometry. Results show that the segmentation is most likely related to the along‐strike variation of the effective normal stress on the fault plane caused by the Yakutat Plateau. The Yakutat Plateau could affect the effective normal stress by either lowering the pore pressure in Upper Cook Inlet due to less fluids release or increasing the normal stress due to the extra buoyancy caused by the subducted Yakutat Plateau. We prefer the latter explanation because it is consistent with the relative amplitudes of the effective normal stress in Upper and Lower Cook Inlet and there is very little along‐strike variation in Vp/Vs ratio in the fault zone from receiver function analysis. However, we cannot exclude the possibility that the difference in effective normal stress results from along‐strike variation of pore pressure due to the uncertainties in the Vp/Vs estimates. Our work implies that a structural anomaly can have a long‐lived effect on the subduction zone slip behavior and might be a driving factor on along‐strike segmentation of slow slip events.

Relationships between along-fault heterogeneous normal stress and fault slip patterns during the seismic cycle: Insights from a strike-slip fault laboratory model

We use a strike-slip fault analog model to study experimentally the role played by along-fault non-uniform and asymmetric applied normal stress on both coseismic slip and long-term fault behavior. Our model is based on a visco-elasto-plastic multi-layered rheology that allows to produce several hundreds of scaled analog microquakes and associated seismic cycles. Uniform or heterogeneous applied normal stress along the fault plane is imposed and maintained constant during the whole experiment durations. Our results suggest that coseismic slip patterns are strongly controlled by spatial normal stress variations and subsequent accumulated shear stress along fault strike. Major microquakes occur preferentially in zones of major shear stress asperities. Coseismic slip distributions exhibit a pattern similar to the along-fault applied normal stress distribution. The occurrence of isolated low to moderate microquakes where residual stresses persist around secondary stress asperities, indicates that stress conditions along the fault also control the whole variability of fault slip events. Moreover, when fault slip stability conditions are modulated by normal stress distribution, our experiments suggest that the along-fault stress heterogeneity influences the seismic cycle regularity and, consequently, long-term fault slip behavior. Uniform applied normal stress favors irregular seismic cycles and the occurrence of earthquakes clustering, whereas non-uniform normal stress with a single high amplitude stress asperity generates strong characteristic microquake events with stable return periods. Together our results strengthen the assumption that coseismic slip distribution and earthquake variability along an active fault may provide relevant information on long term tectonic stress and could thus improve seismic hazard assessment.

Plastic analysis for through silicon via with actual etching defect of triangular-teeth and scallops

Through silicon via (TSV) with triangular-teeth and scalloped side wall (TSSW) not only lowers down the electrical performance but also alters the mechanism of thermal mechanical stability. By considering the realistic etching defects on TSV side wall, a more reasonable and reliable three-dimension (3D) TSV model with TSSW is built. The thermo-mechanical issues induced by the unsmooth side wall of the TSV are studied by finite element method (FEM) in this work. With the presence of TSSW, much more tips in interfaces of the TSV-Cu and SiO2 and the SiO2 and Si are brought and the shear stress and normal stress are distinct comparing with the smooth side wall. Therefore, the thermo-mechanical mechanism of the TSV is changed greatly. By investigating the normal stress, shear stress and strain energy density (SED) of the triangular-teeth local region, it has been found that severe normal stress variation (−200–70MPa) and multiple variation of shear stress τxy contributes the peeling, slip and crack issues. The effective plastic strain, displacement and von Mises stress, and shear stress and normal stress in the X, Y and Z direction are studied in detail. The effect of the TSSW on the thermal stress and keep-out zone (KOZ) size is discussed.

Velocity-dependent characteristics of magnetorheological fluids in squeeze mode considering the hydrodynamic and the magnetic field interactions

This work presents an experimental investigation on the behavior of magnetorheological (MR) fluids in squeeze mode and a theoretical analysis of its MR mechanism. Relative to the well-known large normal stress in squeeze mode, the exciting velocity-dependent characteristics and the normal stress variation tendency of MR fluids are emphasized. The characteristics of MR fluids are tested under displacement-control and force-control modes. It is shown from the tests that along with the exciting velocity, the tensile stress shows an increasing tendency before saturation, but the compressive stress exhibits a decreasing tendency. In addition, under force-control mode (10 N/s) test, after the initial elastic deformation the elastic-plastic deformation occurs instead of plastic flow. As a consequence, in order to fully understand the exciting velocity-dependent characteristics of MR fluids in squeeze mode, a new concept considering both the hydrodynamic interaction between the particles and continuous phase and ...

Effect of moving load due to irregularity in ice sheet floating on water

The present paper is concerned with the stresses produced due to a load moving on the irregular surface of an ice sheet floating on water. The irregularity of the ice medium is of parabolic type, and a rectangular irregularity has also been considered as a special case. The mathematical formulation of this physical problem gives rise to a boundary value problem with the specified boundary conditions. The perturbation method is applied to find the displacement field. Closed-form expressions of the normal and shear stresses developed in the ice medium and semi-infinite water medium due to moving load and irregularity have been derived using the boundary conditions. The variations of dimensionless normal and shear stresses with different depth below the surface are computed for a realistic numerical model and discussed. The same numerical data are used for surface plots to analyze the combined variation of non-dimensional stresses and velocity ratio against depth. From the outcome of the numerical study, the normal and shear stresses developed in both the ice and water media are found to be very sensitive to the changes in frictional coefficient, dimensionless wave number and irregularity factor present in the medium.

Frictional Sliding without Geometrical Reflection Symmetry

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.

An Experimental Study on Normal Stress and Shear Rate Dependency of Basic Friction Coefficient in Dry and Wet Limestone Joints

Among all parameters that affect the friction of rocks, variable normal stress and slip rate are the most important second-order parameters. The shear-rate- and normal-stress-dependent friction behavior of rock discontinuities may significantly influence the dynamic responses of rock mass. In this research, two limestone rock types, which were travertine and onyx marble with slickenside and grinded #80 surfaces, were prepared and CNL direct shear tests were performed on the joints under various shear conditions. The shearing rate varied from 0.1 to 50 mm/min under different normal stresses (from 2 to 30 % of UCS) in both dry and wet conditions. Experiments showed that the friction coefficient of slickensided and ground #80 surfaces of limestone increased with the increasing shear velocity and decreased with the increasing normal stress. Micro-asperity interlocking between ground #80 surfaces showed higher wear and an increase in friction coefficient (µ) compared to slickensided surfaces. Slickensided samples with moist surfaces showed an increase in the coefficient of friction compared to dry surfaces; however, on ground #80 surfaces, the moisture decreased the coefficient of friction to a smaller value. Slickenside of limestone typically slides stably in a dry condition and by stick–slip on moist surfaces. The observed shear-rate- and normal-stress-dependent friction behavior can be explained by a similar framework to that of the adhesion theory of friction and a friction mechanism that involves the competition between microscopic dilatant slip and surface asperity deformation. The results have important implications for understanding the behavior of basic and residual friction coefficients of limestone rock surfaces.

Coupled thermo-poroelastic analysis of drilling induced mechanical damage in fractured rocks

The wellbore represents one of the most crucial components in the hydrocarbon and geothermal reservoir system, as it is the sole conduit to the reservoir for fluid production or injection. Therefore, predicting and controlling of the permeability variations close to the wellbore has been one of the most challenging issues in geothermal and petroleum reservoir systems. A new method is presented to model fracture permeability changes during drilling in fractured rocks. The approach includes finite element method (FEM) for fully coupled thermo-poroelastic analysis of stress distribution around borehole and displacement discontinuity method (DDM) to model fracture deformation. Four models of fracture networks with different facture spacing and varied inclination angle are considered. Permeability variations in underbalanced and overbalanced drilling operations are compared together in different models. The results indicate the difference in effective stress values along x and y directions exceed over 40MPa around borehole and along fracture surface. It was proved that the mechanical stresses caused by excavation of the rock contribute to short time while fluid pressure and thermal stresses contribute to long term permeability change of fractures. The application of the approach illustrates that the maximum variation of fracture aperture occurs near to the borehole and becomes negligible at large distance away from the borehole. Regardless of the drilling operation method, either overbalanced or underbalanced conditions, the permeability of fractures intersecting borehole decreases for large time after drilling. The maximum variations in fracture permeability occur in fracture network with inclination angle of 45 degrees where maximum variation of effective normal and shear stresses occur. Also, initial poroelastic effect of stresses and fluid pressure on the permeability is maximized by increasing fracture spacing.

Multiaxial fatigue of cast aluminium EN AC-42000 T6 (G-AlSi7Mg0.3 T6) for automotive safety components under constant and variable amplitude loading

Regarding the fatigue behaviour of EN AC-42000 T6 (A 356 T6), which is the most frequently used cast aluminium alloy for automotive safety components, especially under non-proportional constant and variable normal and shear stress amplitudes with changing principal stress directions, a poor level of knowledge was available. The reported investigations show that, under non-proportional normal and shear stresses, fatigue life is increased in contrast to ductile steels where life is reduced due to changing principal stress directions. This behaviour caused by the low ductility of this alloy (e < 10%) compared to quenched and tempered steels suggests the application of the Normal (Principal) Stress Hypothesis (NSH). For all of the investigated stress states under multiaxial constant and variable (Gaussian spectrum) amplitudes without and with mean stresses, the NSH was able to depict the life increase by the non-proportionality and delivered, for most cases, conservative but non-exaggerated results.

The structure of slip-pulses and supershear ruptures driving slip in bimaterial friction.

The most general frictional motion in nature involves bimaterial interfaces, when contacting bodies possess different elastic properties. Frictional motion occurs when the contacts composing the interface separating these bodies detach via propagating rupture fronts. Coupling between slip and normal stress variations is unique to bimaterial interfaces. Here we use high speed simultaneous measurements of slip velocities, real contact area and stresses to explicitly reveal this bimaterial coupling and its role in determining different classes of rupture modes and their structures. We directly observe slip-pulses, highly localized slip accompanied by large local reduction of the normal stress near the rupture tip. These pulses propagate in the direction of motion of the softer material at a selected (maximal) velocity and continuously evolve while propagating. In the opposite direction bimaterial coupling favors crack-like ‘supershear' fronts. The robustness of these structures shows the importance of bimaterial coupling to frictional motion and modes of frictional dissipation.

The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics

AbstractWe use 1‐D thermal history models and 3‐D numerical experiments to study the impact of dynamic thermal disequilibrium and large temporal variations of normal and shear stresses on the initiation of plate tectonics. Previous models that explored plate tectonics initiation from a steady state, single plate mode of convection concluded that normal stresses govern the initiation of plate tectonics, which based on our 1‐D model leads to plate yielding being more likely with increasing interior heat and planet mass for a depth‐dependent Byerlee yield stress. Using 3‐D spherical shell mantle convection models in an episodic regime allows us to explore larger temporal stress variations than can be addressed by considering plate failure from a steady state stagnant lid configuration. The episodic models show that an increase in convective mantle shear stress at the lithospheric base initiates plate failure, which leads with our 1‐D model to plate yielding being less likely with increasing interior heat and planet mass. In this out‐of‐equilibrium and strongly time‐dependent stress scenario, the onset of lithospheric overturn events cannot be explained by boundary layer thickening and normal stresses alone. Our results indicate that in order to understand the initiation of plate tectonics, one should consider the temporal variation of stresses and dynamic disequilibrium.

Frictional properties of phyllosilicate‐rich mylonite and conditions for the brittle‐ductile transition

AbstractTo understand frictional properties of natural phyllosilicate‐rich mylonite along fault depth, friction experiments on simulated mylonite gouge were conducted at temperatures of 100–600°C, effective normal stresses of 100–300 MPa, and loading rates of 0.04–1.0 µm/s. Experimental results show that at temperatures above 200°C, frictional strength of the mylonite gouge exhibits systematic increase with temperature, in the range of 0.52–0.73. Under 200–300 MPa normal stress conditions, velocity dependence of mylonite gouge shows a transition from initial velocity‐strengthening (Regime 1) to velocity‐weakening behavior (Regime 2) at a temperature between 200 and 300°C and transitions back to velocity‐strengthening behavior (Regime 3) as temperature increases. The latter transition is also found to be promoted by slower loading rates. Friction stability of the mylonite gouge also exhibits a strong pressure sensitivity. While velocity‐strengthening behavior in Regime 3 is absent under 100 MPa normal stress condition, stable frictional behavior is significantly enhanced at higher effective normal stresses, with the transition temperature to velocity strengthening decreasing with effective normal stress. Microstructural analysis shows that the transition of velocity dependence from velocity weakening to velocity strengthening corresponds to transition from cataclastic flow to semibrittle process featured by mylonitic structures (S‐C fabrics). The formation of mylonitic fabrics is due to plastic deformation of phyllosilicates combined with thermally activated grain size reduction of hard clasts (quartz and plagioclase). Our results may help constrain depth range of seismogenesis within phyllosilicate‐rich fault zone and imply that variation of effective normal stress may affect faulting behavior.

Dynamic instabilities of frictional sliding at a bimaterial interface

Understanding the dynamic stability of bodies in frictional contact steadily sliding one over the other is of basic interest in various disciplines such as physics, solid mechanics, materials science and geophysics. Here we report on a two-dimensional linear stability analysis of a deformable solid of a finite height H, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e. an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number k limit and demonstrate that homogeneous sliding in this case is universally unstable, independent of the details of the friction law. This universal instability is mediated by propagating waveguide-like modes, whose fastest growing mode is characterized by a wave-number satisfying kH∼O(1) and by a growth rate that scales with H−1. We then consider the limit kH→∞ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. In a certain parameter range this instability is manifested through unstable modes at all wave-numbers, yet the frictional response is shown to be mathematically well-posed. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Previous results obtained in the quasi-static regime appear relevant only within a narrow region of the parameter space. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability. The relevance of our results to the rupture of bi-material interfaces is briefly discussed.

Elastodynamic Response of Thermal Laser Pulse in Micropolar Thermoelastic Mass Diffusion Medium

The present investigation deals with the deformation in micropolar thermoelastic diffusion medium due to inclined load subjected to thermal laser pulse. Normal mode analysis technique is used to solve the problem. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The closed form expressions of normal stress, tangential stress, couple stress, temperature distribution, and mass concentration are obtained. A computer program has been developed to derive the physical quantities numerically. The variation of normal stress, tangential stress, coupled stress, temperature change, and mass concentration is depicted graphically to show the effect of relaxation times and mass concentration. Some particular cases of interest are deduced from the present investigation.