The proposed numerical model of machine tool dynamic structure is constructed as a single-loop system consisting of two multi-dimensional links. This approach offers the advantage of considering all the working processes of the machine tool equally and simultaneously by placing them into a single multi-dimensional link. Employing matrix methods of analysis farther enhances the simplicity and universality of this methodology so that modern computer could be used for determining the dynamic qualities of the machine tools. The proposed methodology was validated by tests. The results of these tests are compared with data obtained from proposed computational approach.
{"title":"Dynamic Stability of Multi-Tool Machining","authors":"E. Kushnir, B. Raj","doi":"10.1115/imece1999-0618","DOIUrl":"https://doi.org/10.1115/imece1999-0618","url":null,"abstract":"\u0000 The proposed numerical model of machine tool dynamic structure is constructed as a single-loop system consisting of two multi-dimensional links. This approach offers the advantage of considering all the working processes of the machine tool equally and simultaneously by placing them into a single multi-dimensional link. Employing matrix methods of analysis farther enhances the simplicity and universality of this methodology so that modern computer could be used for determining the dynamic qualities of the machine tools. The proposed methodology was validated by tests. The results of these tests are compared with data obtained from proposed computational approach.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130411892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The eigenvalues of Williams’ series expansion for generalized wedge problems, which include cracks, re-entrant corners, free edges, and cracks meeting with material interface, etc. are examined from the viewpoint of conservation laws like J-integral and M-integral. By use of the so-called two-state conservation laws or interaction energy, originally proposed by Eshelby and later treated by Chen and Shield, discussed is that the complementary pairs of eigenvalues exist in the J-integral sense and/or in the M-integral sense when these integrals are conserved. Similar results are shown to hold for the eigenvalues of three dimensional wedges.
{"title":"Two-State Conservation Integrals and Stress Singularities in Generic Wedges","authors":"S. Im, Youngmin Lee","doi":"10.1115/imece1999-0624","DOIUrl":"https://doi.org/10.1115/imece1999-0624","url":null,"abstract":"\u0000 The eigenvalues of Williams’ series expansion for generalized wedge problems, which include cracks, re-entrant corners, free edges, and cracks meeting with material interface, etc. are examined from the viewpoint of conservation laws like J-integral and M-integral. By use of the so-called two-state conservation laws or interaction energy, originally proposed by Eshelby and later treated by Chen and Shield, discussed is that the complementary pairs of eigenvalues exist in the J-integral sense and/or in the M-integral sense when these integrals are conserved. Similar results are shown to hold for the eigenvalues of three dimensional wedges.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"212 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133921655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses implementation and application of a multiple term viscoelastic constitutive model suitable for plastic materials. The constitutive model uses Feng’s recursive formula where the stress updates depend only on the stress terms in the prior state. The multiple term creep equations are accurate over longer periods of time. A tensile test simulation shows that the model provides reasonable results. Then a press fit example shows the holding force depends on time according to viscoelasticity.
{"title":"A Multiple Term Viscoelastic Constitutive Model Implemented and Applied for Plastic","authors":"R. Verderber, W. W. Feng","doi":"10.1115/imece1999-0621","DOIUrl":"https://doi.org/10.1115/imece1999-0621","url":null,"abstract":"\u0000 This paper discusses implementation and application of a multiple term viscoelastic constitutive model suitable for plastic materials. The constitutive model uses Feng’s recursive formula where the stress updates depend only on the stress terms in the prior state. The multiple term creep equations are accurate over longer periods of time. A tensile test simulation shows that the model provides reasonable results. Then a press fit example shows the holding force depends on time according to viscoelasticity.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"34 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131612973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In an effort to investigate the mechanical properties of shape memory alloy (SMA) fiber reinforced composites, the stress distribution due to the phase change in the fiber is examined. We study a simple model involving a single infinite fiber embedded in an infinite elastic matrix. A portion of the fiber is allowed to undergo uniform phase transformations along the axial direction while the matrix remains linearly elastic. Under perfect bonding condition, the deformation of the fiber forces the matrix to deform in the elastic regime in order to accommodate the transformation strain. To simplify the analysis, the elasticity of the fiber is ignored. The problem is formulated as axisymmetric deformations for the matrix with a piecewise linear boundary condition at the interface with the fiber as a result of the phase transformation in the fiber. The exact elasticity solution (in integral form) to this problem is found using Love’s stress function and Fourier transform. The normalized forms of the solution are presented. The asymptotic behaviors of the stress distributions near the phase boundary are analyzed in details. The characteristics of the singularities near the phase boundary are obtained for this model. Numerical evaluations are also performed to obtain the distributions of the displacements, the strains, and the stresses in the matrix. In particular, the shear load transfer profiles along the interface are obtained for various aspect ratios of the transformed region.
{"title":"Stress Concentration of Shape Memory Alloy Fiber Reinforced Composites in Elastic Axisymmetric Deformations","authors":"Hungyu Tsai, Xin Fan","doi":"10.1115/imece1999-0630","DOIUrl":"https://doi.org/10.1115/imece1999-0630","url":null,"abstract":"\u0000 In an effort to investigate the mechanical properties of shape memory alloy (SMA) fiber reinforced composites, the stress distribution due to the phase change in the fiber is examined. We study a simple model involving a single infinite fiber embedded in an infinite elastic matrix. A portion of the fiber is allowed to undergo uniform phase transformations along the axial direction while the matrix remains linearly elastic. Under perfect bonding condition, the deformation of the fiber forces the matrix to deform in the elastic regime in order to accommodate the transformation strain. To simplify the analysis, the elasticity of the fiber is ignored. The problem is formulated as axisymmetric deformations for the matrix with a piecewise linear boundary condition at the interface with the fiber as a result of the phase transformation in the fiber. The exact elasticity solution (in integral form) to this problem is found using Love’s stress function and Fourier transform. The normalized forms of the solution are presented. The asymptotic behaviors of the stress distributions near the phase boundary are analyzed in details. The characteristics of the singularities near the phase boundary are obtained for this model. Numerical evaluations are also performed to obtain the distributions of the displacements, the strains, and the stresses in the matrix. In particular, the shear load transfer profiles along the interface are obtained for various aspect ratios of the transformed region.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127497680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Damage reduces the flexural stiffness of a structure, thereby altering its dynamic response, specifically the natural frequency, damping values, and the mode shapes associated with each natural frequency. Considerable effort has been put into obtaining a correlation between the changes in these parameters and the location and amount of the damage in beam structures. Most numerical research employed elements with reduced beam dimensions or material properties such as modulus of elasticity to simulate damage in the beam. This approach to damage simulation neglects the non-linear effect that a crack has on the different modes of vibration and their corresponding natural frequencies. In this paper, finite element modeling techniques are utilized to directly represent an embedded crack. The results of the dynamic analysis are then compared to the results of the dynamic analysis of the reduced modulus finite element model. Different modal parameters including both mode shape displacement and mode shape curvature are investigated to determine the most sensitive indicator of damage and its location.
{"title":"Numerical Study for Global Detection of Cracks Embedded in Beams","authors":"Stephen A. Lipsey","doi":"10.1115/imece1999-0616","DOIUrl":"https://doi.org/10.1115/imece1999-0616","url":null,"abstract":"\u0000 Damage reduces the flexural stiffness of a structure, thereby altering its dynamic response, specifically the natural frequency, damping values, and the mode shapes associated with each natural frequency. Considerable effort has been put into obtaining a correlation between the changes in these parameters and the location and amount of the damage in beam structures. Most numerical research employed elements with reduced beam dimensions or material properties such as modulus of elasticity to simulate damage in the beam. This approach to damage simulation neglects the non-linear effect that a crack has on the different modes of vibration and their corresponding natural frequencies. In this paper, finite element modeling techniques are utilized to directly represent an embedded crack. The results of the dynamic analysis are then compared to the results of the dynamic analysis of the reduced modulus finite element model. Different modal parameters including both mode shape displacement and mode shape curvature are investigated to determine the most sensitive indicator of damage and its location.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123274436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Three-dimensional finite element analyses of an elastic-plastic, single rivet-row, aluminum lap joint are presented and compared with previous results for linear elastic models. The calculations treat non-countersunk aluminum and steel rivets, 3 different configurations of countersunk rivets as well as two values of the friction coefficient. The compliance of the connection, rivet tilt, the stresses in the panels, peak plastic strains and the contact pressures and slip amplitudes at the rivet-panel and panel-panel interfaces are evaluated. The transverse, axial, and shear stress distributions and the stress concentrations generated in four different rivets are derived from the linear elastic models and related to the rivet geometry. Laboratory measurements of the lap joint compliance and local out-of-plane displacements that support the reliability of the finite element analyses are presented.
{"title":"Three-Dimensional Analyses of Single Rivet-Row Lap Joints — Part II: Elastic-Plastic Response","authors":"K. Iyer, C. Rubin, G. Hahn","doi":"10.1115/imece1999-0614","DOIUrl":"https://doi.org/10.1115/imece1999-0614","url":null,"abstract":"\u0000 Three-dimensional finite element analyses of an elastic-plastic, single rivet-row, aluminum lap joint are presented and compared with previous results for linear elastic models. The calculations treat non-countersunk aluminum and steel rivets, 3 different configurations of countersunk rivets as well as two values of the friction coefficient. The compliance of the connection, rivet tilt, the stresses in the panels, peak plastic strains and the contact pressures and slip amplitudes at the rivet-panel and panel-panel interfaces are evaluated. The transverse, axial, and shear stress distributions and the stress concentrations generated in four different rivets are derived from the linear elastic models and related to the rivet geometry. Laboratory measurements of the lap joint compliance and local out-of-plane displacements that support the reliability of the finite element analyses are presented.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123724190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In aging aircraft the synergetic interaction between corrosion and fatigue has been shown to impact the life expectancy of aluminum alloys. The objective of this study was to quantify the effects of corrosion, in terms of mass loss, on the static strength and fatigue life of 7075-T6-aluminum alloy. This was an experimental study conducted on samples with laboratory-controlled corrosion of varying mass loss levels at their mid-surface on one side. The specimens were covered with special masking material to allow corrosion only in the desired area. Both fatigue life and the ultimate tensile strength of the specimens were observed to drop significantly with small amounts of mass loss (less than 5%). After the initial decrease the UTS was observed to decrease linearly with additional mass-loss. The fatigue life of the specimens decreased significantly with additional mass loss. The topology of the pits, and the related subsurface damage hinted at existence of areas of high stress concentration resulting in the immediate reduction of UTS and fatigue life of the specimens.
{"title":"Quantification of Corrosion in 7075-T6 Aluminum Alloy","authors":"B. Obert","doi":"10.1115/imece1999-0622","DOIUrl":"https://doi.org/10.1115/imece1999-0622","url":null,"abstract":"\u0000 In aging aircraft the synergetic interaction between corrosion and fatigue has been shown to impact the life expectancy of aluminum alloys. The objective of this study was to quantify the effects of corrosion, in terms of mass loss, on the static strength and fatigue life of 7075-T6-aluminum alloy. This was an experimental study conducted on samples with laboratory-controlled corrosion of varying mass loss levels at their mid-surface on one side. The specimens were covered with special masking material to allow corrosion only in the desired area. Both fatigue life and the ultimate tensile strength of the specimens were observed to drop significantly with small amounts of mass loss (less than 5%). After the initial decrease the UTS was observed to decrease linearly with additional mass-loss. The fatigue life of the specimens decreased significantly with additional mass loss. The topology of the pits, and the related subsurface damage hinted at existence of areas of high stress concentration resulting in the immediate reduction of UTS and fatigue life of the specimens.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126013884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of a three-dimensional interface crack between a film and a substrate to gain a better understanding of how the problem of peeling in film-substrate material systems subjected to thermal loading can be alleviated. We assume that the crack lies in the plane of the interface and is located at one of the free comers of the structure. The fracture parameters (mixed mode stress intensity factors, phase angles and the energy release rate) along the crack front are obtained using an interaction energy integral technique developed by Gosz et al. (1998) for analysis of three dimensional, bimaterial interface cracks. The technique is a very accurate domain integral method that is employed as a post-processing step after a finite element solution for the stress, strain, and displacement fields in the solid has been obtained. In the paper, we investigate the effect of film thickness on the fracture parameters and the results are discussed.
{"title":"Analysis of Interfacial Fracture in Thin Films Subjected to Thermal Loading","authors":"M. Gosz, A. F. Okyar","doi":"10.1115/imece1999-0625","DOIUrl":"https://doi.org/10.1115/imece1999-0625","url":null,"abstract":"\u0000 We consider the problem of a three-dimensional interface crack between a film and a substrate to gain a better understanding of how the problem of peeling in film-substrate material systems subjected to thermal loading can be alleviated. We assume that the crack lies in the plane of the interface and is located at one of the free comers of the structure. The fracture parameters (mixed mode stress intensity factors, phase angles and the energy release rate) along the crack front are obtained using an interaction energy integral technique developed by Gosz et al. (1998) for analysis of three dimensional, bimaterial interface cracks. The technique is a very accurate domain integral method that is employed as a post-processing step after a finite element solution for the stress, strain, and displacement fields in the solid has been obtained. In the paper, we investigate the effect of film thickness on the fracture parameters and the results are discussed.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127442723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A study of the dynamical behavior of aircraft wings modeled as doubly-tapered thin-walled beams, made from advanced anisotropic composite materials, and incorporating a number of non-classical effects such as transverse shear, and warping inhibition is presented. The supplied numerical results illustrate the effects played by the taper ratio, anisotropy of constituent materials, transverse shear flexibility, and warping inhibition on free vibration and dynamic response to time-dependent external excitations. Although considered for aircraft wings, this analysis and results can be also applied to a large number of structures such as helicopter blades, robotic manipulator arms, space booms, tall cantilever chimneys, etc.
{"title":"Dynamic Behavior of Aircraft Wings Modeled as Doubly-Tapered Composite Thin-Walled Beams","authors":"S. Na, L. Librescu","doi":"10.1115/imece1999-0615","DOIUrl":"https://doi.org/10.1115/imece1999-0615","url":null,"abstract":"\u0000 A study of the dynamical behavior of aircraft wings modeled as doubly-tapered thin-walled beams, made from advanced anisotropic composite materials, and incorporating a number of non-classical effects such as transverse shear, and warping inhibition is presented.\u0000 The supplied numerical results illustrate the effects played by the taper ratio, anisotropy of constituent materials, transverse shear flexibility, and warping inhibition on free vibration and dynamic response to time-dependent external excitations. Although considered for aircraft wings, this analysis and results can be also applied to a large number of structures such as helicopter blades, robotic manipulator arms, space booms, tall cantilever chimneys, etc.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122178692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Standard methods of indentation analysis use a beam theory solution to obtain an overall load-displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: previous modeling efforts have shown that the stress distribution in the region of contact will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. In such cases, point contact can no longer be assumed and Hertzian relations are not valid. The indentation model developed herein is an improvement over current GLOBAL/LOCAL approaches in that it uses an elasticity solution to establish the load-displacement relationship at the contact site. The solution technique is applied to two end conditions: (1) simple supports, and (2) fixed ends. Superposition of appropriate elasticity expressions results in systems of Fredholm integral equations of the second kind that are solved numerically. Maximum contact stresses are obtained and compared with the predictions of the previous GLOBAL/LOCAL model. The validity of the solutions presented is assessed by comparing the results obtained to the predictions of modified beam theory solutions.
{"title":"Smooth Asymmetric Indentation of a Finite Elastic Layer","authors":"Minggang Zhou, W. Schonberg","doi":"10.1115/imece1999-0627","DOIUrl":"https://doi.org/10.1115/imece1999-0627","url":null,"abstract":"\u0000 Standard methods of indentation analysis use a beam theory solution to obtain an overall load-displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: previous modeling efforts have shown that the stress distribution in the region of contact will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. In such cases, point contact can no longer be assumed and Hertzian relations are not valid. The indentation model developed herein is an improvement over current GLOBAL/LOCAL approaches in that it uses an elasticity solution to establish the load-displacement relationship at the contact site. The solution technique is applied to two end conditions: (1) simple supports, and (2) fixed ends. Superposition of appropriate elasticity expressions results in systems of Fredholm integral equations of the second kind that are solved numerically. Maximum contact stresses are obtained and compared with the predictions of the previous GLOBAL/LOCAL model. The validity of the solutions presented is assessed by comparing the results obtained to the predictions of modified beam theory solutions.","PeriodicalId":270413,"journal":{"name":"Recent Advances in Solids and Structures","volume":"1966 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129724524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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