Self-Piercing Riveting Process and Joint Modeling and Simulations

Transcription

1 Solids and Structures (SAS) Volume 3, 214 Self-Piercing Riveting Process and Joint Modeling and Simulations M. Grujicic *1, J.S. Snipes 1, S. Ramaswami 1, F. Abu-Farha 2 Departments of: 1 Mechanical Engineering; and 2 Automotive Engineering, Clemson University Clemson, SC 29634, USA * gmica@clemson.edu Received 27 January 214; Accepted 19 May; Published 4 June Science and Engineering Publishing Company Abstract A three-step computational approach is proposed to help establish the effect of various self-piercing riveting (SPR) process and material parameters on the quality and the mechanical performance of the resulting SPR joints. Using the results of a virtual-testing procedure, the constitutive relations for the simified SPR connectors are determined, parameterized and validated. The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash. Keywords Self-Piercing Riveting; Process Modeling; Virtual Testing; Joint Connectors Introduction Self-piercing riveting falls into the category of fast, spot-type, sheet-metal mechanical-fastening processes. In contrast to traditional riveting, self-piercing riveting does not require pre-drilled or pre-punched holes and, therefore, no alignment between the rivet-setting machine and the sheets to be joined is required. Consequently, self-piercing riveting is typically a highspeed, one-step joining process. The results of the SPRprocess modeling disayed in Figures 1(a) (d) reveal the four basic stages (i.e. clamping, piercing, flaring and releasing) of this process. A comprehensive list of the main advantages and few limitations of SPR relative to the alternative joining/fastening technologies can be found in Abe et al. (26). In the same reference, a brief overview of the main areas of apication of SPR can also be found. A review of the open-domain literature carried out as part of the present work revealed a number of experimental studies of the SPR process [Abe et al. (26); Sun and Khaleel (27); Sun et al. (27)]. These studies are focused mainly on the following aspects of this process: (a) an investigation of the effect of various process parameters such as rivet shape/material, worksheet materials and thicknesses, die shape, clamping force, punch force vs. time profile, etc. on the overall structural integrity of the resulting joint; (b) mechanical testing of the joints to determine their static, dynamic and cycling strengths under various combinations of shear and normal-types of loading; and (c) establishment of the functional relationships between the SPR process parameters and the mechanical properties of the riveted joints. Besides real-time monitoring of the punch force vs. time profile during the SPR process, most of the aspects of this joining process could not be monitored (and, thus, controlled) in real time. Consequently, the effect of various SPR process parameters on the quality, structural integrity and mechanical performance of the self-piercing riveted joints relies upon the use of various post-mortem characterization/ measurement techniques. To overcome this limitation, computer modeling of the SPR process has been the subject of a number of investigations. A review of the open-domain literature carried out as part of the present work revealed a number of modeling studies of the SPR process and the structural behavior of the resulting joints [Stühmeyer (25); Sommer and Maier (28)]. The main limitation of these modeling/ simulation studies is that they focus on particular aspects of the process or joint performance. In other words, no attempt is made to relate the SPR process parameters to the SPR-joint mechanical performance as well as with the construction of SPR-joint line connectors used in large-scale computational simulations. 2

2 Solids and Structures (SAS) Volume 3, use of three-dimensional, continuum finite-elementbased numerical simulations of various mechanical tests performed on the SPR joints; and (c) determination and parameterization of the constitutive relations for the simified SPR connectors, using the results obtained in (b). The availability of such connectors is mandatory in large-scale computational analyses of whole-vehicle crash or even in simulations of vehicle component manufacturing, e.g. car-body electro-coat paintbaking process. In such simulations, exicit threedimensional representation of all SPR joints is associated with a prohibitive computational cost. Spr Process Modeling Problem Definition The problem analyzed in this portion of the work involves finite-element analysis of a prototypical SPR joining process. Modeling and Computational Analysis 1) Geometrical Model An exame of the geometrical model/ computational domain for the problem analyzed in this portion of the work is depicted in Figure 1(a). Since the tools (i.e. the punch, the pad and the die) undergo only (small) elastic deformation, they are modeled as rigid bodies, while the rivet and the two sheets are considered as elasto-astic deformable bodies. Furthermore, due to the inherent axisymmetric nature of the region surrounding the rivet axis, the geometrical domain is treated as being axisymmetric. It should be noted that in order to reveal interior details of the computational model, a 3, rather than 36, angular portion of the model is shown in Figure 1(a). 2) Meshed Model FIG. 1. A SCHEMATIC OF THE FOUR BASIC STAGES OF A SINGLE SPR PROCESS CYCLE, CALLED: (A) CLAMPING; (B) PIERCING; (C) FLARING; AND (D) RELEASING. The main objectives of the present work include: (a) finite-element modeling and simulations of the SPR process; (b) determination of the mechanical properties of the resulting SPR joints through the The mesh size, within different components, used in the SPR-process modeling was determined by carrying out a mesh-sensitivity analysis and represents a compromise between the computational efficiency and accuracy. Typically, the meshed model contained between ca. 3, and 1, quadrilateral us triangular axisymmetric elements with finer elmements being used in the top/bottom sheet regions near the rivet. 3) Computational Algorithm All the calculations carried out in this portion of 21

3 Solids and Structures (SAS) Volume 3, 214 the work are based on a transient, disacementbased, purely-lagrangian, conditionally-stable, exicit finite-element algorithm [Grujicic et al. (27, 213)]. Since the SPR process is generally not associated with significant thermal effects, such effects are neglected in the present work. 4) Initial Conditions At the beginning of the analysis, all the components of the computational model are assumed to be stationary, and the deformable components are assumed to be stress-free. 5) Boundary Conditions The following boundary conditions were apied to the computational domain: (a) Punch A time-dependent downward ( zdirection) disacement was prescribed. (b) Pad A time-dependent downward holdingforce was apied. (c) Die Cometely fixed with respect to all its translational and rotational degrees of freedom. (d) Rivet, top sheet and bottom sheet Only the boundary conditions consistent with the axisymmetric character of the problem are prescribed. 6) Contact Interactions Punch/rivet, pad/top-sheet, top-sheet/bottom-sheet, rivet/sheets and bottom-sheet/die interactions are all modeled using the penalty-type normal-contact algorithm combined with a generalized Coulomb friction law [Grujicic et al. (212a, 214)]. 7) Material Models Since the punch, pad and die are all treated as rigid bodies, and a dynamic analysis was carried out, the only material property required for these components is their mass density. The mechanical response of the rivet and sheets is assumed to be governed by the same isotropic (linearly) elastic, and (strain-hardenable, strain-rate sensitive, thermally-softenable) astic constitutive model (with different parameterizations). Furthermore, it is assumed that this response can be mathematically represented using the Johnson- Cook material-model formulation. To enable piercing of the top and bottom sheets by the rivet, in addition to the deformation model, a progressive damage model had to be defined for the sheets to be joined. This was accomished by emoying the classical Johnson-Cook progressivedamage/ductile-failure model. Typical Results The results presented in this subsection were obtained for the following set of process/material parameters [Porcaro et al. (26b)]: (a) sheets material: A 66 T4 and T6; (b) sheet thicknesses 2 mm; (c) Boellhoff rivet C 5 x 6 made of high strength steel; (d) Boellhoff DZ die; (e) stroke-control piercing as defined in Figure 2; and (f) time-dependent clamping force as defined in Figure 2. Punch Stroke, mm Punch Stroke Clamping force Time, s FIG. 2. PROCESS-MODELING INPUT FUNCTIONAL RELATIONSHIPS SHOWING TEMPORAL EVOLUTION OF PUNCH STROKE AND CLAMPING FORCE. Spatial distribution of the attendant materials during the SPR process is shown in Figures 1(a) (d). The four previously mentioned stages of this process can be readily identified by examining the results disayed in these figures. Figure 3 depicts the results pertaining to the functional relationship between the punch force (output) and the punch stroke (input). Examination of the results disayed in Figure 3 reveals that initially, as the rivet is piercing the top sheet, the increase in the magnitude of the (negative) punch force is relatively small. However, as the rivet penetrates the bottom sheet, approaches the rigid die, and begins to flare, the punch-force magnitude increases at a progressively higher rate. Virtual Mechanical Testing of SPR Joints The self-piercing riveting process is associated with a relatively large number of process and material parameters (e.g. rivet geometry and material, top and bottom sheet-metal materials and thicknesses, die Clamping Force, kn 22

4 Solids and Structures (SAS) Volume 3, profile, etc.). Consequently, optimization of the SPR process with respect to obtaining the desired combination of the SPR-joint properties, using purely experimental means, is generally impractical or even infeasible. To help overcome this problem, virtual mechanical testing of the SPR joints can be emoyed. Punch force, kn Punch stroke, mm FIG. 3. PROCESS MODEL OUTPUT SHOWING THE PUNCH FORCE VS. PUNCH STROKE FUNCTIONAL RELATIONSHIP. Problem Definition The problem analyzed in this portion of the work deals with virtual mechanical testing of the SPR joints. Four types of virtual mechanical tests are used: (a) normal-pull test; (b) shear test; (c) 45 oblique-pull test; and (d) peel test. Modeling and Computational Analysis The virtual mechanical-testing procedure emoyed in the present work utilizes the same type of finiteelement formalism as the one described in the previous section. 1) Geometrical Model Exames of the geometrical models used in the aforementioned four virtual mechanical tests are depicted in Figures 4(a) (d). It should be noted that in these cases the geometrical models are no longer axisymmetric, but instead, possess a vertical ane of symmetry. The test-specimen geometries differ only in the number (one or two, per sheet), location (top/bottom, left/right) and orientation (vertical vs. oblique) of the bent end sections. These end sections are used for specimen gripping during virtual testing. Geometrical boundaries for the rivet and for the upper and lower sheets (in the vicinity of the rivet joint) are obtained by mapping the material-distribution results of the axisymmetric finite-element modeling of the SPR process to a full three-dimensional computational domain. The remainder of the upper and lower sheets are reconstructed by simy assuming that their geometries/thicknesses were not affected by the SPR process. The vertical and oblique end sections are obtained by bending the sheet ends over a 4. mm-radius rigid/immobile rod. For each test specimen, the direction of the apied loading is indicated, in Figures 4(a) (d), using arrows, and the (vertical) symmetry ane is labeled. 2) Meshed Model Since the geometrical models depicted in Figures 4(a) (d) are not axisymmetric, the computational model had to be treated and meshed as a threedimensional body. Consequently, the computational domain for each of the four test- specimen geometries is meshed using continuum eight-node, first-order hexahedron elements with reduced integration. The mesh size in the vicinity of the SPR joint was chosen to match the corresponding mesh size used in the SPR-process model. Sections of the upper and lower sheets further away from the SPR joint, including the vertical/oblique sections, are modeled using a coarser mesh. 3) Computational Algorithm The same computational algorithm as the one used for SPR-process modeling is emoyed in this portion of the work. 4) Initial Conditions Since the SPR process is associated with extensive astic deformation of the rivet and the two sheets and introduces residual stresses and damage into the region surrounding the joint, the astic strain, residual stress and damage fields obtained at the end of the SPR-process modeling had to be mapped onto the test specimens and used as initial conditions. 5) Boundary Conditions For all four test specimen geometries, symmetry boundary conditions are apied along the vertical symmetry ane. In adition, constant-velocity loading is apied in the test-specific direction, as indicated in Figures 4(a) (d). The velocity-type loading is apied to the affected faces of the test specimen using a translator-type connector (a connector in which the only available degree of freedom 23

5 Solids and Structures (SAS) Volume 3, 214 freedom of the nodes residing on the subject surface to the corresponding degrees of freedom of a reference node, i.e. the node which coincides with one of the connector nodes). The stiffness of the translator connector is then selected in such a way as to match the combined stiffness of the loading piston and the specimen-gripping device. 6) Contact Interactions The same contact algorithm as the one used for SPR process modeling is emoyed in this portion of the work. 7) Material Models The same material models as those used for SPR process modeling are emoyed in this portion of the work. However, as mentioned above, the rivet and sheet materials are assigned initial values of astic deformation and damage in accordance with the results obtained at the end of the SPR process modeling. Typical Results Figures 5(a) (d) show typical results pertaining to the spatial distribution and temporal evolution of the rivet, top-sheet and bottom-sheet materials during the normal-pull test. Examination of the results disayed in Figures 5(a) (d) reveals that: (a) during the test, the rivet is being pulled out from the bottom sheet while still attached to the top sheet; and (b) in this process, the bottom sheet experiences most of the damage while the top sheet suffers substantially less damage. Typical load vs. disacement curves obtained in this portion of the work for the normal-pull, shear, 45 oblique-pull, and peel tests are depicted in Figures 6(a) (d) and labeled as 3-D SPR Joint. The results disayed in these figures will be discussed in the next section, when they will be compared with their counterparts obtained using the shell representation of the sheets and connector representation of the rivet. Construction of the SPR-Joint Connectors Problem Definition FIG. 4. GEOMETRICAL MODELS USED IN THE SPR-JOINT VIRTUAL MECHANICAL TESTING: (A) NORMAL-PULL; (B) SHEAR; (C) 45 OBLIQUE-PULL; AND (D) PEEL TEST SPECIMENS. is the translation of the two nodes along the line connecting them) and a couing-type kinematic constraint (a constraint which coues the degrees of The problem analyzed in this portion of the work involves derivation, parameterization and validation of the governing equations of the SPR-joint connectors. Derivation of the Line-type SPR-Joint Connector Constitutive Relations The constitutive relations for the SPR-joint connector are 24

6 Solids and Structures (SAS) Volume 3, (sixth) DOF; (e) astic behavior of the connector is described in a manner similar to the conventional metal asticity and involves specifications of the yield potential, flow rule and the hardening/constitutive relations; and (f) damage initiation and damage evolution relations are assumed to mimic those encountered in the case of ductile failure involving voids nucleation, growth and coalescence. 1) Elastic behavior In accordance with the assumptions made above, as well as regarding free rotation about the connector axis (x3), the elastic response of the SPR connector is fully defined by using five elastic stiffnesses Ei, i = 1 5 (E6=). 2) Plastic behavior The driving force promoting astic response of the connector is assumed to be governed by the following yield-potential function: P β β 1 β FN FS = + RN RS (1) where the equivalent normal force, F N, and equivalent shear force, F S, are respectively defined as: K 2 2 FN = f3 + m1 + m2 (2) r S F = f + f (3) FIG. 5. AN EXAMPLE OF THE RESULTS PERTAINING TO THE SPATIAL DISTRIBUTION AND TEMPORAL EVOLUTION OF THE RIVET, TOP-SHEET AND BOTTOM-SHEET MATERIALS DURING THE PULL TEST. derived under the following conditions, assumptions and simifications: (a) a local connector coordinate system is used, within which the connector is aligned in the x3-direction, while directions x1 and x2 lie in the ane of the riveted sheets; (b) elastic responses of the connector associated with each of the three translational and rotational degrees of freedom (DOFs) are assumed to be independent/decoued; (c) the riveted joint is assumed to be axisymmetric; (d) since the riveted joint can be readily rotated about its axis of symmetry, zero elastic stiffness is assigned to this where i = 1, 2, 3 denotes three components of a vector associated with the three coordinate axes, f denotes a force, m a moment, r is the rivet radius, and R N, R S, β and K are the connector yieldpotential parameters. The onset and continuation of the astic response is then assumed to be governed by the following yield criterion: ( f, f, f, m, m ) F ( u ) φ = P (4) where F is the force-equivalent of the yield strength, and u is the equivalent astic relative motion (a quantity analogous to the equivalent astic strain in metal asticity). Evolution of the astic relative motion T u = u1, u2, u3, ur1, u r2 (where subscript r denotes a rotational DOF) is assumed to be 25

7 Solids and Structures (SAS) Volume 3, 214 governed by the associated/normality flow rule as: φ u = u. (5) f where the generalized force vector is defined as [ f, f, f, m m ] T f = , 2. The equivalent astic relative motion rate and the equivalent astic relative motion are then defined as: T ( ) ( ) φ φ u. u T. f f u = (6) = t u u dt (7) Eq. (7) yields u = RS u1 for the case of pure shear in direction 1 and u = RN u3 for the case of pure tension in the axial direction x3. As astic deformation proceeds, the connector is assumed to experience isotropic strain-hardening. Consequently, F in Eq. (4) controls the size of the (fixed-shape) yield surface. As astic deformation proceeds, u and, thus, F increase, causing an expansion of the yield surface. Thus, hardening behavior is fully described by the F vs. u functional relationship. FIG. 6. A COMPARISON OF THE LOAD VS. DISPLACEMENT RESULTS OBTAINED IN THE VIRTUAL TESTING OF SOLID SPR-JOINTS AND SHELL-SECTIONS RIVETED BY SPR-JOINT CONNECTORS: (A) NORMAL-PULL; (B) SHEAR; (C) 45 OBLIQUE-PULL; AND (D) PEEL TESTS. 26

8 Solids and Structures (SAS) Volume 3, ) Damage Initiation and Evolution As astic deformation continues, the equivalent astic relative motion crosses a critical value beyond which the connector continuously incurs internal damage. Both the critical value of u and the rate of damage evolution/accumulation are generally found to be functions of the connector loading angle (i.e. loading mode-mixity) Ψ m, defined as: 2 1 F Ψ = N m tan π FS Clearly, Ψ m =. for the case of pure shear, and Ψ m = 1. for the case of pure normal loading. Damage initiation is then fully defined by a udi vs. Ψ m functional relationship, where subscript DI denotes damage initiation. As internal damage accumulates within the connector, its strength is assumed to decrease linearly with an increase in u. At u = u f, connector strength becomes zero, causing it to fail. Under this simifying assumption, damage evolution is fully defined by a ( u f udi ) vs. Ψ m relation. Parameter Identification and Calibration In the cases of normal-pull, pure-shear and 45 oblique-pull loading, the contribution of the bending moments m 1 and m 2 to the overall loading is negligibly small. Since the contribution of the bending moments to the overall loading is proportional to the parameter K in Eq. (2), the results of these tests are first used to determine the remaining parameters and functional relations defining the connector constitutive behavior. Then, the peel-test results are used to determine K. (8) 2) Plastic Behavior To determine R S and R N, the following procedure was emoyed: (a) It is first established that the initial level of the connector strength, F, is independent of the mode of loading; (b) At the peak load under normal-pull, pure-shear and 45 oblique-pull loading, the connector acquires the same (maximum) level of its strength, F max ; and (c) By combining Eqs. (1) and (4), the following I relation: FI = FJ RJ, I =, max, J = N, S is obtained. Using this relation, the astic portions of the force vs. disacement curves (up to the onset of damage), and a curve-fitting procedure, R N = 2.3 and R S = are obtained. The parameter β is obtained by curve-fitting the 45 oblique-pull force vs. disacement results in the astic region (up to the onset of failure) to the relation obtained by combining Eqs. (1) and (4). This procedure yielded β = The F vs. u relationship is obtained by: (i) extrapolating the elastic response of the connector into the elastic/astic region; and (ii) estimating the astic relative disacement (as a difference between the total and the elastic relative disacements) at different levels of F. This procedure yielded the functional relationship F vs. u depicted in Figure 7. 1) Elastic Behavior Using the elastic portions of the force vs. disacement results obtained under normal-pull, pure-shear and 45 oblique-pull loading conditions, and emoying a curve-fitting procedure, the first three elastic-stiffness constants are determined as follows: E1 = E2 = 2.97 MN/m and E3 = 3.54 MN/m. Following prior work of Weyer et al. (26), E4 and E5 are assumed to be infinite (a rigid-elastic approximation). FIG. 7. STRENGTH VS. RELATIVE PLASTIC DISPLACEMENT HARDENING BEHAVIOR OF THE SPR-JOINT CONNECTOR. 27

9 Solids and Structures (SAS) Volume 3, 214 3) Damage Initiation and Evolution To define the udi vs. Ψ m functional relationship, it was first assumed that damage initiates at the point of maximum load. Then the sought-after functional relationship is obtained by simy determining the equivalent astic relative disacement associated with the corresponding peak loading for different tests, each corresponding to a different value of Ψ m. The resulting udi vs. Ψ m functional relationship is depicted in Figure 8. Equivalent astic motion at damage initiation FIG. 8. THE EFFECT OF MODE MIXITY ON THE EQUIVALENT PLASTIC MOTION AT DAMAGE INITIATION, AND THE ADDITIONAL POST-DAMAGE-INITIATION EQUIVALENT PLASTIC MOTION AT THE POINT OF FAILURE. To calibrate the ( u ) u f DI vs. Ψ m functional relationship, it is first recognized that in the postdamage-initiation portion of the load vs. disacement curves, the mixity ratio changes during loading (except for the cases of pure normal and pure shear loading). Taking this into account, combining all the post-damage-initiation force vs. disacement data, and utilizing a linear regression analysis, the piecewise linear form of the ( u f udi ) vs. Ψ m functional relationship depicted in Figure 8 is obtained. 4) Parameter K in Eq. (2) Mode Mixity To determine the last unknown parameter K, an optimization procedure was emoyed in conjunction with the finite-element simulations (for the peel test) as described in the next section. Within these simulations, riveted sheets are modeled as shell structures while the SPR-joint is Difference of equivalent astic motion modeled as the connector constructed and parameterized in this section. Within the optimization procedure, parameter K was used as a single design variable while the extent of agreement between the peel-test load vs. disacement results obtained in the previous section and in the present section was defined as the objective function. This procedure yielded K =.53. Validation Procedure To validate the fidelity of the derived and parameterized constitutive relations for the SPR-joint connectors (described above), virtual (normal-pull, shear, 45 oblique-pull and peel) tests of riveted shelltype specimens are carried out. In these simulations, the riveted connections between the sheets are represented using the just-derived SPR-joint connectors. Temporal evolution of the material within the two riveted shells during the pull test is depicted in Figures 9(a) (b). A comparison of these results with their counterparts in Figures 5(b) (d) reveals that in both cases, the ultimate failure of the SPR joint takes ace by the degradation and fracture of the (mainly bottom) sheet material surrounding the rivet. This was an expected outcome since the bottom sheet has acquired the largest extent of damage during the SPR process. (b) FIG. 9. TEMPORAL EVOLUTION OF THE MATERIAL WITHIN THE TWO RIVETED SHELLS DURING THE PULL TEST. Figures 6(a) (d) disay the load vs. disacement results (labeled as SPR-Joint Connector ) for the normal-pull, shear, 45 oblique-pull and peel tests obtained in this portion of the work. A comparison of the two sets of results reveals that the overall level of agreement for each of the four tests is satisfactory, relative to the joint strength (as quantified by the maximum force), joint ductility (as quantified by the maximum disacement before a comete loss of the load-carrying capacity), and the overall toughness (as (a) 28

10 Solids and Structures (SAS) Volume 3, quantified by the area under the load vs. disacement curve). This finding suggests that the SPR-joint connectors can reasonably well account for the mechanical response of the very detailed threedimensional continuum SPR joints. Summary and Conclusions Based on the results obtained in the present work, the following main summary remarks and conclusions can be drawn: (a) a three-step computational procedure is developed to establish dependence of the mechanical properties of the self-piercing rivets (SPRs) on the SPR process parameters; (b) this procedure involves finiteelement modeling and simulations of the SPR process and virtual testing of the resulting SPR joints under different types of loading such as normal-pull, shear, 45 oblique-pull and peeling; (c) the results of the virtual mechanical testing are used to construct and parameterize SPR-joint point-to-point line-connector elements. These elements are used in large-scale simulations of whole-vehicle crash in the vehicle-body manufacturing process (e.g. car-body electro-coat paint-baking process); and (d) virtual testing of the shell components riveted using the joint connectors validated the ability of these line elements to realistically account for the strength, ductility and toughness of the three-dimensional SPR-joints. REFERENCES Abe, Y., Kato, T., and Mori, K. "Self-piercing riveting of high tensile strength steel and aluminium alloy sheets using conventional rivet and die." Journal of Materials Processing Technology 29 (29): Grujicic, M., Pandurangan, B., Zecevic, U., Koudela, K.L., and Cheeseman, B.A. Ballistic Performance of Alumina/S-2 Glass-Reinforced Polymer-Matrix Composite Hybrid Lightweight Armor Against Armor Piercing (AP) and Non-AP Projectiles." Multidisciine Modeling in Materials and Structures 3 (27): Grujicic, M., Arakere, A., Pandurangan, B., Yen, C.-F., and Cheeseman, B.A. Process Modeling of Ti-6Al-4V Linear Friction Welding (LFW)." Journal of Materials Engineering and Performance 21 (212): Grujicic, M., Galgalikar, R., Snipes, J. S., R. Yavari, Ramaswami, S. Multi-Physics Modeling of the Fabrication and Dynamic Performance of All-Metal Auxetic-Hexagonal Sandwich-Structures. Materials and Design 51 (213): Grujicic, M., Yavari, R., Snipes, J. S., Ramaswami, S., Yen, C.- F., and Cheeseman, B. A. Linear Friction Welding Process Model for Carpenter Custom 465 Martensitic Precipitation-Hardened Stainless Steel. Journal of Materials Engineering and Performance (214). DOI: 1.17/s Porcaro, R., Hanssen, A.G., Langseth, M., and Aalberg, A. " Self-piercing riveting process: An experimental and numerical investigation." Journal of Materials Processing Technology 171 (26b): 1 2. Stühmeyer, A. "Self-piercing riveting." Paper presented at the 5th LS-DYNA European Conference, Birmingham, UK, 25. Sommer, S., and Maier, J., Failure modeling of a selfpiercing riveted joint using LS-DYNA, Paper presented at the 8th LS-DYNA European Conference, Strasbourg, France, 28. Sun, X., and Khaleel, M. A. "Dynamic strength evaluations for self-piercing rivets and resistance spot welds joining similar and dissimilar metals." International Journal of Impact Engineering 34 (27): Sun, X., Stephens, E. V., and Khaleel, M.A. "Fatigue behaviors of self-piercing rivets joining similar and dissimilar sheet metals." International Journal of Fatigue 29 (27): Weyer, S., Hooputra, H., Zhou, F., Modeling of Self- Piercing Rivets Using Fasteners in Crash Analysis, Paper presented at the 26 ABAQUS Users Conference, Cambridge, MA, USA. 29