Strain Rate Gradient Research Articles

Evolution of Flame Curvature in Turbulent Premixed Bunsen Flames at Different Pressure Levels

The physical mechanisms underlying the curvature evolution in turbulent premixed Bunsen flames at different thermodynamic pressures are investigated using a three-dimensional Direct Numerical Simulation database. It is found that, due to the occurrence of the Darrieus-Landau instability, the high-pressure flame exhibits higher probability of developing large negative curvature values and saddle concave topologies than the low pressure cases. The terms in the curvature transport equation due to normal strain rate gradients and curl of vorticity arising from both turbulent flow and flame normal propagation play pivotal roles in the curvature evolution. The mean value of the net contribution of the flame propagation terms dominates over the net contributions arising from the background fluid motion. The net contribution of the source/sink terms tries to reduce the convexity of the flame surface in the positively curved locations. By contrast, the net contribution of the source/sink terms promotes concavity of the flame surface towards the reactants in the negatively curved regions and this effect is particularly strong for the high pressure flame, where the effects of the Darrieus-Landau instability are prominent. This also gives rise to large negative skewness of the probability density functions of curvature in the high-pressure flame with the Darrieus-Landau instability.

Characterization of Anisotropic Damage Behaviour of Recycled Aluminium Alloys AA6061 Undergoing High Velocity Impact

It is impossible to ignore the realm of the topics related recycling aluminium scraps. The recycled form of this material can be a good replacement for the primary resources due to the economic and environmental benefits. Numerous investigation must be conducted to establish the mechanical behaviour before the specific applications can be identified. In this research, Taylor Cylinder Impact tests used to investigate anisotropic damage behaviour in recycled aluminium alloy is presented. To be specific, by performing Taylor Cylinder Impact test at velocities ranging from 190m/s to 300m/s, anisotropic and damage characteristics can be observed in the samples as a function of the large stress, strain, and strain-rate gradient. The application of Taylor Cylinder Impact test as a technique to validate both the constitutive and dynamic fracture responses in such materials is also discussed. The structure of recycled aluminium AA6061 including the damage initiation and evolution are observed under optical microscope (OM) and scanning electron microscope (SEM). The results revealed that the damage evolution of the material change with the increasing impact velocity. Further, the digitised footprint analysis showed a pronounced anisotropic characteristic of the recycled aluminium AA6061.

Effects of Lewis Number on the Evolution of Curvature in Spherically Expanding Turbulent Premixed Flames

The effects of Lewis number on the physical mechanisms pertinent to the curvature evolution have been investigated using three-dimensional Direct Numerical Simulation (DNS) of spherically expanding turbulent premixed flames with characteristic Lewis number of L e = 0.8 , 1.0 and 1.2. It has been found that the overall burning rate and the extent of flame wrinkling increase with decreasing Lewis number L e , and this tendency is particularly prevalent for the sub-unity Lewis number (e.g., L e = 0.8 ) case due to the occurrence of the thermo-diffusive instability. Accordingly, the L e = 0.8 case has been found to exhibit higher probability of finding saddle topologies with large magnitude negative curvatures in comparison to the corresponding L e = 1.0 and 1.2 cases. It has been found that the terms in the curvature transport equation due to normal strain rate gradients and curl of vorticity arising from both fluid flow and flame normal propagation play pivotal roles in the curvature evolution in all cases considered here. The net contribution of the source/sink terms of the curvature transport equation tends to increase the concavity and convexity of the flame surface in the negatively and positively curved locations, respectively for the L e = 0.8 case. This along with the occurrence of high and low temperature (and burning rate) values at the positively and negatively curved zones, respectively acts to augment positive and negative curved wrinkles induced by turbulence in the L e = 0.8 case, which is indicative of thermo-diffusive instability. By contrast, flame propagation effects tend to weakly promote the concavity of the negatively curved cusps, and act to decrease the convexity of the highly positively curved bulges in the L e = 1.0 and 1.2 cases, which are eventually smoothed out due to high and low values of displacement speed S d at negatively and positively curved locations, respectively. Thus, flame propagation tends to smoothen the flame surface in the L e = 1.0 and 1.2 cases.

Contemporary crustal tectonic movement in the southern Sichuan-Yunnan block based on dense GPS observation data

We analyzed 360 permanent and campaign GPS data from 1999 to 2017 in the southern Sichuan-Yunan block, and obtained crustal horizontal deformation in this region. Then, we derived the strain rate using a multi-scale spherical wavelet method. Results reveal a complex pattern of tectonic movement in the southern Sichuan-Yunnan block. Compared to the stable Eurasian plate, the maximum rate of the horizontal deformation in the southern Sichuan-Yunnan block is approximately 22 mm/a. The Xiaojiang fault shows a significantly lower deformation—a left-lateral strike-slip movement of 9.5 mm/a. The Honghe fault clearly shows a complex segmental deformation from the north to south. The northern Honghe fault shows 4.3 mm/a right strike-slip with 6.7 mm/a extension; the southern Honghe fault shows 1.9 mm/a right strike-slip with 1.9 mm/a extension; the junction zone in the Honghe and Lijiang–Xiaojinhe faults shows an obvious clockwise-rotation deformation. The strain calculation results reveal that the maximum shear-strain rate in this region reaches 70 nstrain/a, concentrated around the Xiaojiang fault and at the junction of the Honghe and Lijiang–Xiaojinhe faults. We note that most of the earthquakes with magnitudes of 4 and above that occurred in this region were within the high shear strain-rate zones and the strain rate gradient boundary zone, which indicates that the magnitude of strain accumulation is closely related to the seismic activities. Comparison of the fast shear-wave polarization direction of the upper-crust with the upper-mantle anisotropy and the direction of the surface principal compressive strain rate obtained from the inversion of the GPS data reveals that the direction of the surface principal compressive strain is basically consistent with the fast shear-wave polarization direction of the upper crust anisotropy, but different from the polarization direction of the upper mantle. Our results support the hypothesis that the principal elements of the deformation mechanism in the southern Sichuan-Yunnan block are decoupling between the upper and lower crust and ductile flow in the lower crust.

Thermal gradient and its contribution to size effect of specific cutting energy

The size effect of specific cutting energy is one of the most fundamental and challenging problems in metal cutting. The size effect phenomenon has been attributed to the material strengthening effect due to strain, strain rate, and strain gradient. However, the contribution of the material strengthening caused by temperature effect in the primary shear zone is rarely studied. Here, orthogonal cutting experiments under different initial temperature were conducted. It shows the significant dependence of the size effect phenomenon on the temperature effect. The finite element methods were further conducted to reveal the underlying reason of the size effect. It is found that there exists high-temperature gradient in the primary shear zone along the shear direction, which causes the average temperature in the primary shear zone to drop with decreased uncut chip thickness, giving rise to the size effect phenomenon. Furthermore, a new approach is developed to predict the highest temperature in the primary shear zone by numerical fitting.

Hemodynamic Factors Affecting Carotid Sinus Atherosclerotic Stenosis

Carotid atherosclerotic plaque occurs predominantly at the outer wall of the carotid sinus, and computational fluid dynamics (CFD) plays an important role in explaining plaque formation. The present study investigated the hemodynamic factors affecting carotid atherosclerotic stenosis. Sixteen patients with normal carotid arteries and 16 with symptomatic stenotic carotid sinus underwent 3-dimensional angiographic imaging evaluations and were studied with CFD to simulate the complete 3-dimensional blood flow and hemodynamic parameter distribution in the carotid bifurcations. The hemodynamic parameters, including wall shear stress (WSS), dynamic and total pressure, total pressure gradient, strain rate, velocity, and velocity angle, were investigated. The atherosclerosis-prone outer lateral walls of the carotid sinus and the external carotid artery at its start had significantly (P < 0.05) low dynamic pressure, WSS, strain rate, and total pressure gradient but high static pressure. The blood flow near these walls with flow separation had significantly (P < 0.05) decreased velocity and dynamic pressures but a high velocity angle. The carotid divider had significantly (P < 0.05) elevated dynamic and total pressure, WSS, strain rate, and total pressure gradient but reduced static pressure. Additional stenosis occurred at the downstream area of stenosis with significantly (P<0.05) decreased dynamic pressure, WSS, strain rate, and total pressure gradient similar to the wall at the sinus and the start of the external carotid artery. Significantly decreased vascular WSS, dynamic pressure, strain rate, and total pressure gradient are key to atherosclerotic plaque formation at the carotid sinus.

Normal fault growth in layered basaltic rocks: The role of strain rate in fault evolution

Conceptual models for the evolution of dilatant faults in volcanic rift settings involve a step-wise growth pattern, involving upward propagation of subsurface faults, and surface monocline formation, which are breached by subvertical, open faults. Immature, discontinuous normal faults are considered representative of the early stages of mature, linked faults that accommodate extensional strains. We consider the evolution of surface-breaking normal faults using a comparison of the distribution and geometry of normal faults from two volcanic rift zones: the Koaʻe fault system, Hawaiʻi, and the Krafla fissure swarm, NE Iceland. Field mapping highlights similarities to current predicted geometries, but also prominent differences that are not reconciled by current models. Variable deformation styles record magma supply changes within the rift zones, which drive local strain rate gradients. Building on existing studies, we present a conceptual model of fault growth that accounts for spatial and temporal changes in strain rate within the deforming regions. We propose that faults in separate rift systems may not advance through the same stages of evolution and that faults within individual rift systems can show differing growth patterns. Variations in surface strains may be indicative of subsurface magmatic system changes, with important implications for our understanding of volcano-tectonic coupling.

Fabrication of nanostructure in inner-surface of AISI 304 stainless steel pipe with surface plastic deformation

In the present investigation, a pipe inner-surface grinding (PISG) technique was developed to fabricate nanostructure in the inner-surface of an austenitic 304 stainless steel pipe. PISG was performed by high speed shearing with hard sphere tips, leading to gradient distribution of strain, strain rate and strain gradient along depth. Nano-austenite with an average boundary spacing of 20 nm was generated, followed by deformation microstructure characterized by shear bands, multi- and uni-directional twins and planar dislocation arrays. Deformation induced grain refinement of austenitic 304 stainless steel with low stacking fault energy (SFE) covering 4–5 order’s magnitude of length scales toward nanometer regime was unified.

Strain-induced microstructure refinement in pure Al below 100 nm in size

The obtainable minimum structural size and microstructural characteristics of pure Al processed by three different deformation techniques, i.e., cold rolling (CR), dynamic plastic deformation (DPD) and surface mechanical grinding treatment (SMGT), have been investigated by means of transmission electron microscope and orientation mapping. A systematic evaluation of the effects of deformation parameters on structural refinement was performed, mainly focusing on the microstructures at high strains. In contrast to the submicro-scale laminated structures from CR at ambient temperature, which are mainly composed of high angle grain boundaries, deformation at low temperature and high strain rate facilitates formation of high density low angle grain boundaries (LAGBs) in DPD and SMGT samples. With a combination of low temperature, high strain rate and large strain gradient, nanolaminated (NL) structures with a size of only ∼68 nm and a large fraction of LAGBs (∼65%) was fabricated by means of SMGT. NL Al exhibits a record high Vickers hardness of 780 MPa, which has its origin in the capability of accommodating high density dislocations in the form of LAGBs. This study provides an alternative approach to design nanostructures below the traditional refinement limit by generating more LAGBs.

An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems

This article considers a plane strain gradient plasticity theory of the Gurtin?Anand model [M. Gurtin, L. Anand, A theory of strain gradient plasticity for isotropic, plastically irrotational materials Part I: Small deformations, J. Mech. Phys. Solids 53 (2005), 1624?1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin?Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.

Application of a strain rate gradient microfluidic device to von Willebrand's disease screening.

Von Willebrand's disease (VWD) is the most common inherited bleeding disorder caused by either quantitative or qualitative defects of von Willebrand factor (VWF). Current tests for VWD require relatively large blood volumes, have low throughput, are time-consuming, and do not incorporate the physiologically relevant effects of haemodynamic forces. We developed a microfluidic device incorporating micro-contractions that harnesses well-defined haemodynamic strain gradients to initiate platelet aggregation in citrated whole blood. The microchannel architecture has been specifically designed to allow for continuous real-time imaging of platelet aggregation dynamics. Subjects aged ≥18 years with previously diagnosed VWD or who presented for evaluation of a bleeding disorder, where the possible diagnosis included VWD, were tested. Samples were obtained for device characterization as well as for pathology-based testing. Platelet aggregation in the microfluidic device is independent of platelet amplification loops but dependent on low-level platelet activation, GPIb/IX/V and integrin αIIbβ3 engagement. Microfluidic output directly correlates with VWF antigen levels and is able to sensitively detect aggregation defects associated with VWD subtypes. Testing demonstrated a strong correlation with standard clinical laboratory-based tests. Head-to-head comparison with PFA100® demonstrated equivalent, if not improved, sensitivity for screening aggregation defects associated with VWD. This strain rate gradient microfluidic prototype has the potential to be a clinically useful, rapid and high throughput-screening tool for VWD as well as other strain-dependent platelet disorders. In addition, the microfluidic device represents a novel approach to examine the effects of high magnitude/short duration (ms) strain rate gradients on platelet function.

Near-surface mechanical heterogeneities in a dissimilar aluminum alloys friction stir welded joint

The local mechanical properties of a dissimilar friction stir welded AA-2024-T3/AA-2198-T3 joint were documented during a uniaxial tensile test. High-resolution digital image correlation was performed during monotonic tensile tests to capture the local in-plane strain fields of the heterogeneous macrostructure of the weld. In the shoulder-affected region, banded macrostructures with heterogeneous mechanical properties were found. They were related to pronounced textures regions, which can be associated to strain-rate gradient during one rotation of the tool. The banded macrostructures in the nugget region were observed to be responsible for early plasticity in the joint and ultimately to be the fracture location of the weld. The heterogeneous mechanical response of the joint was also investigated by microhardness measurements. Differences were found between hardness and local tensile properties, demonstrating microhardness measurements can be misleading and only direct high-resolution digital image correlation techniques can document the mechanical behavior of materials having complex and heterogeneous micro-/macrostructures.

Baroclinic instability of axially symmetric flow over sloping bathymetry

Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical two-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Non-zero barotropic flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

Abstract 17131: Diastolic Dysfunction in Asymptomatic Patients With Moderate to Severe Aortic Regurgitation is Strongly Related to Increased Longitudinal Fiber Stress and Subsequent Non-uniform Myocardial Relaxation

Introduction: Diastolic dysfunction in aortic regurgitation (AR) is present at an early stage of the disease. Yet, the mechanisms are not clearly understood. Hypothesis: We hypothesized that diastolic dysfunction in AR patients is caused by increased longitudinal (meridional) fiber stress and subsequent impaired relaxation of the corresponding subendocardial (longitudinal) fibers. Methods: Thirty asymptomatic patients with moderate to severe aortic regurgitation (AR) and 17 age matched healthy controls (C) where analyzed (32 ± 7 and 35 ± 4 (SD) years, respectively, p=NS) with 3D speckle tracking echocardiography. We measured early diastolic longitudinal- (LSRe) and circumferential (CSRe) strain rate (1/s) as the time derivative of strain (%) and the peak difference (LSRe – CSRe) during isovolumic relaxation (IVR). Early diastolic flow rate (sec -1 ) was estimated as the time derivative of the LV volume curve normalized to end-diastolic volume (EDV). Finally, we calculated end-systolic meridional fiber stress (mmHg). Results: LV ejection fraction in C and AR was 61 ± 2 and 62 ± 3 %, respectively (p=NS). AR patients had signs of impaired LV filling with lower early diastolic flow rate (Table 1). During IVR, the strain rate curves consistently departed (Figure 1, arrow), indicating a non-homogenous relaxation. A negative correlation was shown between meridional fiber stress and the IVR strain rate gradient (y= -0.0123x + 1.0921, r=0.61, p&lt;0.001). Conclusions: We have demonstrated a non-homogenous relaxation of subendocardial- relative to circumferential fibers in AR patients that strongly correlated with longitudinal fiber stress, suggesting a causal relationship.

Comparison of Material Flow Stress Models toward More Realistic Simulations of Friction Stir Processes of Mg AZ31B

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

Comparison of Material Flow Stress Models toward More Realistic Simulations of Friction Stir Processes of Mg AZ31B

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

Edelen’s dissipation potentials and the visco-plasticity of particulate media

Following is an elaboration on D. G. B. Edelen’s (1972–1973) nonlinear generalization of the classical Rayleigh-Onsager dissipation potentials and the implications for the models of viscoplasticity. A brief derivation is given via standard vector calculus of Edelen’s potentials and the associated non-dissipative or “gyroscopic” forces and fluxes. It is also shown that certain extensions of Edelen’s formulae can be obtained by means of a recently proposed source-flux relation or “inverse divergence,” a generalization of the classical Gauss-Maxwell construct. The Legendre–Fenchel duality of Edelen’s potentials is explored, with important consequences for rate-independent friction or plasticity. The use of dissipation potentials serves to facilitate the development of viscoplastic constitutive equations, a point illustrated here by the special cases of Stokesian fluid-particle suspensions and granular media. In particular, we consider inhomogeneous systems with particle migration coupled to gradients in particle concentration, strain rate, and fabric. Employing a mixture-theoretic treatment of Stokesian suspensions, one is able to identify particle stress as the work conjugate of the global deformation of the particle phase. However, in contrast to past treatments, this stress is not assumed to be a privileged driving force for particle migration. A comparison is made with models based on extremal dissipation or entropy production. It is shown that such models yield the correct dissipative components of force or flux but generally fail to capture certain non-dissipative, but mechanically relevant components. The significance of Edelen’s gyroscopic forces and their relation to reactive constraints or other reversible couplings is touched upon. When gyroscopic terms are absent, one obtains a class of strongly dissipative or hyperdissipative materials whose quasi-static mechanics are governed by variational principles based on dissipation potential. This provides an interesting analog to elastostatic variational principles based on strain energy for hyperelastic materials and to the associated material instabilities arising from loss of convexity.

Finite element modelling of superplastic-like forming using a dislocation density-based model for AA5083

Superplastic-like forming is a newly improved sheet forming process that combines the mechanical pre-forming (also called hot drawing) with gas-driven blow forming (gas forming). Non-superplastic grade aluminium alloy 5083 (AA5083) was successfully formed using this process. In this paper, a physical-based material model with dislocation density and vacancy concentration as intrinsic foundations was employed. The model describes the overall flow stress evolution of AA5083 from ambient temperature up to 550 °C and strain rates from 10−4 up to 10−1 s−1. Experimental data in the form of stress–strain curves were used for the calibration of the model. The calibrated material model was implemented into simulation to model the macroscopic forming process. Hereby, finite element modelling (FEM) was used to estimate the optimum strain-rate forming path, and experiments were used to validate the model. In addition, the strain-rate controlled forming was conducted for the purpose of maintaining the gas forming with an average strain rate of 2 × 10−3 s−1. The predicted necking areas closely approximate the localized thinning observed in the part. Strain rate gradients as a result of geometric effects were considered to be the main reason accounting for thinning and plastic straining, which were demonstrated during hot drawing and gas forming by simulations.

A Strain-Rate Gradient Theory of Plasticity and its Comparison with Strain Gradient Theories

Gradient theories of plasticity play an important role in the description of inelastic behavior of materials. Usually, these theories involve space derivatives of stress or strain. On the other hand, conventional theories of plasticity can be divided into two groups, flow and deformation theories. Each of these groups has its own area of applications. The main conceptual difference between the theories belonging to the different groups is that the primary kinematics variables in deformation theories are displacements (or strains) whereas in flow theories velocities (or strain rates). Therefore, it is of interest to propose a gradient theory of plasticity involving space derivatives of a measure of strain rate (strain-rate gradient theory of plasticity) and to compare qualitative behavior of solutions for the strain-rate gradient theory of plasticity and an existing strain gradient theory of plasticity. One possible strain-rate gradient theory of plasticity is proposed in the present paper. The equivalent strain rate (second invariant of the strain rate tensor) is used as a measure of strain rate. The Laplacian operator is adopted to introduce the gradient term. An analytic solution for expansion of a hollow sphere is given for two strain-rate gradient theories of plasticity and one strain gradient theory. Comparison of the solutions shows that some qualitative features of the solutions for the strain-rate gradient theories are in better agreement with general physical expectations than those for the strain gradient theory.

Strain, strain rate and velocity fields determination at very high cutting speed

High speed imaging is used for the purpose of examining the strain and strain rate variations in the primary shear zone at cutting speed of 1020m/min. Experimental investigation focused on flow pattern describing the severe plastic deformation zone where a general streamline model is employed to investigate the distribution of velocity. Strain and strain rate distribution are directly deduced from the experimental observation of a cross-section of chip obtained through a high-speed camera system. The strain and strain rate gradients were analyzed along several streamlines. A finite element method model based on a Lagrangian formulation has been used to corroborate the conclusion of the streamline model. It has been found that the simulation results are similar to the experimental observations with regards to the magnitude of the equivalent strain rate and cumulative plastic strain but slightly differ in the geometry of flow pattern.