Stress Equilibrium Conditions Research Articles

Novel bulk triaxial residual stress mapping in an additive manufactured bridge sample by coupling energy dispersive X-ray diffraction and contour method measurements

A novel approach for determining triaxial residual stress states by coupling energy dispersive X-ray diffraction and contour method measurements is provided and validated in a Ti‐5Al‐5V‐5Mo‐3Cr additive manufactured (AM) bridge sample. Synchrotron X-ray diffraction (SXRD) can provide relatively fine spatial resolution (on the order of 10–100 µm) for mapping 3D elastic strain fields within a sample. However, for samples with dimensions larger than one or two centimeters the path length can get prohibitive as both constant wavelength and energy dispersive SXRD are based upon transmission measurements. As an example, for a plate-like sample geometry where the thickness is limited (less than a centimeter) it is trivial to measure the longitudinal and height direction elastic strain components with excellent in-plane spatial resolution (∼100 µm) and a somewhat lower through-thickness resolution (10–15 times larger) but obtaining the through thickness component is often not possible as the beam path must be parallel to one of the large dimensions of the plate. While small samples of low Z-number alloys (e.g., Ti or Al) allow determination of the three elastic strain components, this is often not the case for higher Z alloys (e.g., Fe or Ni) or large samples where some strain components can be indeterminable. To overcome these limitations, this work applies a combination of synchrotron X-ray diffraction and the contour method (a mechanical relaxation technique), to determine the triaxial stress state. This novel combination is demonstrated and validated in a relatively small additive manufactured sample where all three orthogonal strain components are accessible via X-ray diffraction for stress determination. The paper also explores methods for determining the strain-free lattice parameter, typically obtained from a small stress-free reference sample. This work shows that a small size AM sample is not stress free, producing unreliable magnitudes of strain and stress. Instead, a strain-free lattice parameter is determined using residual stress equilibrium conditions, which gives consistent strain and stress trends for both X-ray diffraction (alone) and the new diffraction-contour coupling technique. This demonstrates that the coupling technique can be confidently applied to samples to determine stress when path length (size or Z-number) prohibit determination of three orthogonal strain components via diffraction.

Interface Engineering and Electron-Hole Wave Function Overlap of InAs/AlSb Superlattice Infrared Detectors

InAs/AlSb is a material system that can be used as a low-noise avalanche detector and operates in the short-wave infrared band. The interface parameters determine the wave function overlap (WFO). Maximizing the WFO of InAs/AlSb superlattices improves the quantum efficiency (QE) of infrared avalanche photodetectors (APDs). However, this remains a huge challenge. Here, the 8-band k·p perturbation method based on Bloch wave envelope function approximation was used to calculate the energy level structure of InAs/AlSb superlattices. The results indicate that the WFO is enhanced with increasing InSb interface thickness or when the InSb (or AlAs) interface is far from the intersection of InAs and AlSb. As the AlAs interface thickness increases, the WFO enhances and then reduces. The maximum increase in WFO is 15.7%, 93%, and 156.8%, respectively, with three different models. Based on the stress equilibrium condition, we consider the interface engineering scheme proposed for enhancing WFO with an increase of 16%, 114%, and 159.5%, respectively. Moreover, the absorption wavelength shift is less than ±0.1 μm. Therefore, the interface layer thickness and position can be designed to enhance the WFO without sacrificing other properties, thereby improving the QE of the device. It provides a new idea for the material epitaxy of APDs.

Effect of neutral layer migration on bending force of AZ31B magnesium alloy sheet during bending

In this paper, they are based on the micro-element stress equilibrium condition in the plastic deformation theory and the Yoon-2014 yield criterion, which can reflect the tension and compression asymmetry of AZ31B magnesium alloy, a bending force model is established to predict the required bending force at different angles according to the neutral layer migration in the bending process of magnesium plate. The offset and bending force values of the neutral layer were verified by FEM and corresponding experiments. The results show that the bending force of a magnesium plate is related to the geometrical size of the scale, the yield limit of the material, and the height of the elastic zone of deformation. The model’s prediction accuracy is better than that of the conventional calculation formula, which can realize the reliable prediction of the required bending force of the magnesium plate. In the bending process, the magnesium plate is affected by the asymmetry of tension and pressure, and the neutral layer migrates to the tensile side. The deviation degree of the neutral layer is the most obvious when the magnesium plate is bent to 90°, and the required bending force is the largest.

On the Construction of Mathematical Models of the Membrane Theory of Convex Shells

Introduction. The paper considers the issues of constructing mathematical models of the momentless equilibrium stress state of elastic convex shells using methods of the complex analysis. At the same time, shells with a piecewise smooth (ribbed) lateral surface were considered for the first time. The work objective was to find classes of shells for which it is possible to build meaningful mathematical models.Materials and Methods. Using the methods of the theory of the discontinuous Riemann-Hilbert problem for generalized analytic functions, a criterion for the unconditional solvability of the corresponding static problem for the equilibrium equation of a convex shell with a ribbed lateral surface has been obtained. This criterion, combined with the methods of the theory of generalized analytical functions, is a tool for constructing mathematical models of the state of momentless stress equilibrium of elastic convex shells.Results. A method has been developed for constructing mathematical models of the momentless equilibrium stress state of a convex shell under the action of a variable external load and the condition of stress concentration at the corner points of the median surface. The introduction of a vector parameter, as well as the concepts of “order of quasi-correctness” and “quasi-stability”, into the boundary condition provided both quantitative and qualitative comparison of mathematical models. Classes of shells have been found for which the description of mathematical models is given in terms of the geometry of the boundary in the vicinity of the corner points of the median surface. The obtained result, when applied to shallow convex shells, provides a geometric criterion of quasi-stability. It is established that for a shallow shell, which is not quasi-stable, the only adequate mathematical model is a probabilistic one.Discussion and Conclusions. The proposed method for constructing a two-parameter family of problems with a modified boundary condition makes it possible to simulate the momentless equilibrium stress state for fairly wide classes of convex shells with a piecewise-smooth lateral surface under a sleeve connection. At the same time, the developed algorithm for calculating the boundary condition index allowed us to answer the question of the existence of an adequate mathematical model for a shell with a side surface of an arbitrary configuration, and for shells of a special type (specifically, shallow or shells of revolution), to formulate a geometric criterion for the existence of a mathematical model.

Assessing the impact of underground working (tunneling) in the II section of Seam 14 on surface construction works at Ha Lam Coal Mine (Vietnam)

Purpose. Tunneling in the ground changes the initial equilibrium stress state of the rock, which is also the cause of displacement and deformation of the surrounding rock mass. To determine the impact of tunneling on surface construction works in order to ensure the safety of surface works by analyzing the displacements and deformations of the rock mass during tunneling in the IIsection of Seam 14 at Ha Lam Coal Mine. Methodology. To achieve the research results, actual field survey methods, data analysis and numerical modeling, as well as combined blasting vibration methods are used. Findings. After analyzing the numerical modeling results, an area has been identified in the II section of Seam 14 of the Ha Lam Coal Mine that affects the surface construction works and is located within a radius of about 20 m from the portal of two inclined shafts. The results of blasting vibrations are calculated on the basis of the passport of blasting operations in tunnels. Thus, the affected area has been identified within a radius of 30.5m. However, at a distance of 30.5 m, surface construction works are not in the area of influence. Originality. On the basis of FLAC software, the authors have developed a simulation model for tunneling, thereby analyzing and describing the best state of deformation and displacement of the surrounding rock mass. In this study, a numerical modeling method is applied to simulate the driving order for each tunnel, which is consistent with the actual production of underground mines. Based on the passport of drilling and blasting operations in tunnels, the authors calculated the impact of blasting vibrations on surface construction works. After that, the authors assessed and identified the affected area with the required degree of reliability. Practical value. The research results are used as a basis for implementation in actual production at Ha Lam Coal Mine. On the basis of analysis of the surrounding rock mass displacements and deformations, when tunneling in the II section of Seam 14 at Ha Lam Coal Mine, the affected area of the surface construction works has been determined. This is also the basis for Ha Lam Coal Mine when planning construction works on the site outside the determined affected areas to ensure the safety of such works.

Some consequences of the distributional stress equilibrium condition

We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First, we obtain the local equilibrium conditions in the bulk and at the interface, the latter inclusive of interfacial stress and stress dipole fields. Second, we obtain the necessary and the sufficient conditions on the divergence-free non-smooth stress field for there to exist a stress function field such that the stress equilibrium is trivially satisfied. In doing so, we allow the domain to be non-contractible with mutually disjoint connected boundary components. Both derivations illustrate the utility of the theory of distributions in dealing with singular stress fields.

An analytical model for predicting the shear strength of unsaturated soils

The prediction of shear strength of unsaturated soils remains a significant challenge due to their complex multi-phase nature. In this paper, a review of prior experimental studies is first presented in order to outline important pieces of evidence, limitations and some design considerations. Then, an overview of existing shear strength equations is summarised, with a brief discussion. A micromechanical model with stress equilibrium conditions and multi-phase interaction considerations is presented to provide a new equation for predicting the shear strength of unsaturated soils. The validity of the proposed model is examined using published shear strength data for different soil types. The shear strength predicted by the analytical model was found to be in good agreement with the experimental data and to provide high performance in comparison with existing models. Evaluation of the results using two criteria – the average relative error and the normalised sum of squared error – proved the effectiveness and validity of the proposed equation. Using the proposed model, a non-linear relationship between shear strength, saturation degree, volumetric water content and matric suction was observed.

Geometrically exact beam element with rational shear stress distribution for nonlinear analysis of FG curved beams

Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams. In order to accurately predict the distribution of transverse shear stress, the stress equilibrium condition is introduced into the element formulation by using the mixed finite element method with displacements and internal forces as independent fields. The element nodal force vector and consistent tangent stiffness matrix for nonlinear iterative solution are obtained by going through a consistent linearization procedure. Numerical examples are presented to validate the present formulation. As indicated by the numerical results, the proposed element demonstrates a high level of solution accuracy and good applicability. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of FG structures with different material distribution parameters, and the accuracy loss caused by unreasonable distribution of shear stress is discussed.

Finite Element Analysis on Mixed-Mode Dynamic Fracture Experiments of Centrally Cracked Brazilian Disks With Crack Face Contact

To verify the feasibility of measuring brittle material’s complex-mode dynamic fracture toughness, the centrally cracked Brazilian disk (CCBD) specimen was tested under dynamic loads in the split Hopkinson pressure bar (SHPB) system in view of crack face contact. The 3D SHPB-CCBD finite element model was established to calculate dynamic stress intensity factors (DSIFs) of the CCBD specimen under different loading conditions. Results show that, the fracture time condition of stress equilibrium is necessary for calculating DSIFs through extension of the quasi-static stress intensity factor (SIF) formula with crack face contact to the dynamic expression. The crack face contact leads to changes of the crack face stress, and has a significant impact on the mode-II DSIFs. The test values of mode-II DSIFs will be unreasonably larger without regard to the crack face contact.

Mechanical Properties and Failure Modes of Thick-Walled Cylinder Granites with Different Apertures under Triaxial Compression

Roadway excavation changes the original equilibrium stress state of the rock mass, resulting in the loading and unloading of the surrounding rock near the free surface. After the excavation, the tangential stress increases and the radial stress decreases, which mainly cause deformation and collapse of the roadway. In order to study the strength characteristics of the surrounding rock after the excavation, one effective way is to carry out triaxial compression tests on small surrounding rock samples. Therefore, this paper focuses on the triaxial compression mechanical propertiesof thick-walled cylinder granites with an electrohydraulic, servo-controlled rock mechanics testing system (MTS-815). It studies how different pore sizes and confining pressures affect the triaxial compressive strength (TCS), deformation, and failure modes of granite samples. The results are as follows: (1) Under triaxial compression, the stress-strain curves have no obvious yield stage, and the peak TCS increases with the confining pressure (σ3). When σ3 is low, there is little difference in the TCS between the complete specimen and the thick-walled cylinders. When σ3 reaches 30 MPa∼40 MPa, the TCS of samples with apertures of 15 mm and 20 mm are obviously lower. The σ3 has an obvious influence on the elastic modulus of thick-walled cylinder granites. (2) Shearing and splitting are the main failure modes under triaxial compression. When σ3 is low, shear failure appears. As σ3 reaches 30 MPa∼40 MPa, split failure occurs. The area of the fracture surface increases with σ3. (3) As σ3 grows, the influence parameter (m) of the three-dimensional Hoek-Brown criterion increases. Under the same σ3, the value of m presents a decreasing trend from the outer wall to the inner wall, which means the bearing capacity keeps getting lower and lower. As a result, the inner wall is most likely to be damaged. The theoretical analysis results agree well with the tests.

Consolidation of unsaturated composite ground reinforced by permeable columns

Abstract In this paper, the governing equations and semi-analytical solutions are proposed to investigate the consolidation behavior of unsaturated composite ground with the permeable columns. Based on the stress and strain equilibrium conditions of composite ground and the strain–stress relations of unsaturated soils under the axisymmetric condition, a set of the basic equations are proposed for describing the strain–stress relations of soil element, air and water phases of unsaturated soils in the composite ground. Then, two consolidation equations for air and water phases are derived considering the continuity of pore volume change, and flow laws for air and water phases under the axisymmetric condition. Correspondingly, the semi-analytical solutions of the consolidation equations are proposed by using the Laplace and finite Hankel transforms. The proposed governing equations as well as the semi-analytical solutions are verified by checking against the existing ones for a special case in the literature. Finally, a parametric study is performed to investigate the consolidation behavior with different parameters for the permeable columns and surrounding unsaturated soils.

Microscopic stresses in carbon nanotube reinforced aluminum matrix composites determined by in-situ neutron diffraction

One of the most desired strengthening mechanisms in the carbon nanotube reinforced aluminum matrix composites (CNT/Al) composites is the load transfer strengthening mechanism (LTSM). However, a fundamental issue concerning the LTSM is that quantitative measurements of load partitioning in these composites during loading are very limited. In this study, in-situ neutron diffraction study on the tensile deformation of the 3 vol.% CNT/2009Al composite and the unreinforced 2009Al alloy was conducted. The {311} and {220} diffraction elastic constants (DECs) of the 2009Al alloy were determined. Using those DECs the average stress in the 2009Al matrix of the composite was calculated. Then the average stress in the CNTs was separated by using the stress equilibrium condition. Computational homogenization models were also applied to explain the stress evolution in each phase. Predicted results agree with experimental data. In the present case, the average stress in the CNTs reaches 1630 MPa at the yield strength of the composite based on linear regression of the measured data, which leads to an increment of yield strength by about 37 MPa. As the result of this work, an approach to quantify load partitioning in the CNTs is developed for the CNT/Al composites, which can be applied to optimize the mechanical properties of the composites.

A novel testing technique for dynamic mechanical properties of inorganic glass by electromagnetic Hopkinson bar

Optical glass materials have a lot of superior properties such as outstanding optical transparency, light weight, low manufacturing cost and high impact resistance. Thus, they are widely utilized in the transparent armors, windshields of high-speed train and airplane as well as mobile phone touch screens. Glass structures are often subjected to loading, including quasi-static and dynamic loading during their service. It is well known that the mechanical properties of engineering materials under impact loading are usually much different from those under static loading. To guide the optimal design of glass structures, it is necessary to conduct a thorough and in-depth study of the mechanical properties of glass materials. However, as a kind of typical brittle material, the failure strain of inorganic glass is extremely small. Therefore, measuring the dynamic mechanical properties of glass material has always been a quite difficult problem in the fields of experimental mechanics and impact dynamics. This paper would propose a new experimental technique-electromagnetic split Hopkinson pressure bar (ESHPB) to solve the afore-mentioned problem. In this paper, quasi-static compressive tests were first conducted using the electronic universal testing machine at a strain rate 10–3 s–1, followed by dynamic unidirectional and bidirectional compressive tests by the ESHPB apparatus under an average strain rate of 300 s−1 for soda-lime silicate glass, respectively. During dynamic compressive tests, the ultra-high-speed camera and flashlights were utilized to observe the damage/crack initiation, propagation and fracture process inside the glass samples. The feedback signal of the ultra-high-speed camera is input into the digital acquisition system, aiming to associate accurately the stress history of the sample with the high-speed image and to study the dynamic failure process in depth. The following conclusions are made based on the test results: (1) When using the ESHPB set-up to measure the dynamic mechanical properties of glass materials, stress equilibrium and approximate constant strain rate loading condition can be achieved without using the pulse shaping technique. It provides a simpler and easier test method for studying the dynamic mechanical properties of brittle materials. (2) Compared with the unidirectional loading tests, bidirectional symmetric loading experimental technique can significantly shorten the time duration for achieving the condition of stress equilibrium and constant strain rate deformation. Therefore, more effective information can be obtained from the test results and the accuracy and reliability of the test results can be greatly improved. (3) Compared with the quasi-static test results, it is found that the compressive strength of the tested glass material increases significantly under dynamic impact loading, showing a strong strain rate effect. The dependence of compressive strength on strain rate was quantitatively characterized by the strain rate sensitivity exponent. (4) The deformation images of samples captured by ultra-high-speed camera indicated that when the cracks first appeared, the specimens did not completely lose the load bearing capacity. The cracks continue to nucleate, propagate and converge. When the cracks fill almost the entire sample, the material loses the load bearing capacity completely and breaks into powders. By comparison, the samples are split into a few columns under quasi-static loading.

Post-cyclic undrained response of sand and silt

Cyclic loading of saturated soils is often accompanied by pore pressure accumulation, the magnitude of which, has a tendency to significantly affect the post-cyclic characteristics. This study discusses the post-cyclic behaviour of fine sand and low plastic silt in laboratory testing. Different levels of excess pore pressure ratios were first allowed to develop in the samples during undrained cyclic loading. These samples were then permitted to drain and reach a new equilibrium stress state, before subjecting them to undrained monotonic loading. These findings show that post-cyclic recompression disturbed the soil's structure and changed the gradient of its original unloading-reloading line. The effect of this disturbance was greater in samples which were previously close to liquefaction. The strength improvement in sand grains was less compared to the improvement observed in silt-sized grains. The results nonetheless imply that the post-cyclic recompression strength can be related to the excess pore pressure developed prior, during the cyclic loading.

A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams

In this paper, a new higher-order shear deformation beam theory is developed by introducing the stress equilibrium condition. On the basis of the new shear deformation theory, novel shear deformable mixed beam elements with independent internal force fields and displacement fields are developed for accurate analysis of the functionally graded sandwich beams. Furthermore, a shear deformable beam element with additional interpolated axial displacement is also constructed in order to get reliable reference solutions. Two examples are presented to investigate the solution accuracy of different beam elements. Numerical results indicate that the present mixed beam elements can accurately predict the stress distributions over the cross section and ultimately give accurate displacement solutions. Moreover, the characteristics of axial displacement distributions and transverse shear strain distributions for functionally graded sandwich beams are discussed and the difficulty of getting accurate solutions by introducing a single form higher-order displacement function is pointed out. In these cases, the equilibrium-based beam theory and the corresponding mixed beam elements are more effective and reliable to obtain accurate solutions. Finally, the numerical stability for different beam elements is investigated and the results indicate the present higher-order shear deformable mixed beam element has excellent numerical stability.

The dynamic asymmetric fracture test and determination of the dynamic fracture toughness of large-diameter cracked rock specimens

We propose large-diameter (160 mm) pre-cracked chevron notched Brazilian disc (P-CCNBD) specimens were used to study the asymmetric fracture law and determine the dynamic fracture toughness of rock. Specimens were diametrically impacted by a split Hopkinson pressure bar. The dynamic fracture failure process of each specimen was monitored by crack propagation gauges and strain gauges. Each of the large-diameter P-CCNBD specimens was found to exhibit prominent asymmetric fracture under impact load. The stress equilibrium condition cannot be satisfied. The dynamic fracture toughness values of the rocks were measured using the experimental-numerical method rather than the quasi-static method. The calculation results showed that the dynamic fracture toughness of rocks increases with the dynamic loading rate. In addition, at the 3-D crack front, the dynamic stress intensity factor was found be substantially different at each point. These data suggest that the dynamic fracture toughness of P-CCNBD specimens should be calculated by removing the value affected by an edge arc crack and taking the average value of the remaining points.

Evaluation of the Stress Equilibrium Condition in Axially Constrained Triaxial SHPB Tests

Over the years many improvements and modifications have been made to the split Hopkinson pressure bar (SHPB). For example, the triaxial SHPB has been developed and used to study various materials. The dynamic stress equilibrium condition for conventional SHPB tests has been well studied in the literature. However, the stress equilibrium in the axially constraint triaxial SHPB tests requires careful examination because the wave propagation is affected by the axial pre-load stress. In this study, we analyzed the stress equilibrium condition in such cases using stress wave analysis and numerical simulations. Based on the study, we offer methods and suggestions for performing valid stress equilibrium assessment in axially constrained triaxial SHPB tests.

Constant Strain Rate Uniaxial Compression of Green Sandstone during SHPB Tests Driven by Pendulum Hammer

During the Split-Hopkinson pressure bar (SHPB) tests driven by pendulum hammer, employing a proper special shape striker is an effective way to obtain dynamic stress equilibrium condition and to get constant strain rate of the rock specimen. To find the proper special shape striker, a striker with a cambered surface was introduced and eight geometrically different hammers were designed to analyze the effect of hammer geometry on the waveform of excited incident stress waves. Based on experiments and simulations, parameter effects, including the cambered hammer curvature radius and hammer diameter, length, and impact velocity, on the incident wave shape were examined. These parametric studies provided guidelines for achieving constant strain rates in rock specimens during SHPB tests. The use of different diameter hammers was noted for shaping stress-time curves to follow the stress-strain behavior of green sandstone. Finally, to examine the applicability of using hammer geometry for shaping incident waves to achieve constant strain rate, SHPB tests on green sandstone specimens were conducted. The results demonstrated that a constant strain rate (100 s−1) lasting for 70 μs was achieved with the 8# hammer (3.7 kg; curvature radius, diameter, and length of 100, 70, and 126.3 mm, resp.). In addition, dynamic experiments on green sandstone were carried out under various strain rates and the results showed that the initial tangential modulus was almost unaffected by strain rate. The strain at peak stress tended to increase with rising strain rate and the dynamic strength of green sandstone showed an apparent rate dependency.

Swelling Behavior of Bentonite-Based Backfilling Materials in Nuclear Waste Repository Conditions

During the postconstruction phase, the stress equilibrium conditions within the proposed underground nuclear waste repositories may alter because of various factors, such as far-field mining activity, fluctuation of the groundwater table, and seepage erosion. A reduction in the transmitted stress from the host rock may destabilize the isochoric condition, leading to swelling displacement of backfilling and buffer materials. In the current study, the swelling behavior of bentonite-based backfilling materials was studied. Laboratory tests were carried out on compacted bentonite (dry density=1.26 Mg/m3) and bentonite-sand (70% bentonite, 30% sand, dry density=1.50 Mg/m3) specimens in a strain-controlled oedometer. First, compacted specimens were hydrated with distilled water under constant volume condition. Next, predetermined displacements were introduced in a step-wise manner that caused expansion of the specimens. The swelling pressures of the specimens were measured under a constant-volume condition at each induced strain. The test results showed that induced strains caused a decrease in the swelling pressures of the saturated backfilling materials. A decrease in the swelling pressure for a maximum induced strain of approximately 1.6% was found to be approximately 19% for the bentonite specimen and approximately 30% for the bentonite-sand specimen. It was shown how the swelling index of backfilling materials can be used to assess the recoverable swelling pressure following any induced strain.

Determination of macroscopic and microscopic residual stresses in friction stir welded metal matrix composites via neutron diffraction

This study presents a new method to determine both the macroscopic and microscopic (including elastic mismatch, thermal misfit and plastic misfit) residual stresses in metal matrix composite (MMC) welds via neutron diffraction. As an illustration, friction stir welded 17vol.% SiCp/2009Al-T4 plates were investigated. It is shown that the calculation of the thermal misfit plus plastic misfit residual stresses in the metal matrix of the MMC welds is much more accurate by using the absolute unstrained lattice parameter of the SiC powder sample based on the stress equilibrium condition compared with using that of the unreinforced alloy sample. The profiles of the longitudinal (L), transverse (T) and normal (N) components of the total residual stress in the reinforcement are entirely different from those in the matrix. It was found that the profiles and total variations of the L, T and N components of the total residual stress are dominated by those of the macroscopic residual stress in the matrix, and by those of the elastic mismatch residual stress in the reinforcement, revealing a significant load transfer from the matrix to the reinforcement. The maximum total residual stress in the metal matrix of the FSW 17vol.% SiCp/2009Al-T4 weld could reach up to ∼69% of the yield strength of the 2009Al-T4 alloy. Increasing the rotation rate has small effects on the basic profiles of the total residual stress, apart from increasing the width of the profiles.