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A new concept for the description of surface friction phenomena
Journal of Materials Processing Technology 94 (1999) 189±192
A new concept for the description of surface friction phenomena E. Doege, C. Kaminsky*, A. Bagaviev Institut fuÈr Umformtechnik und Umformmaschinen, UniversitaÈt Hannover, Welfengarten 1A, 30167 Hannover, Germany Accepted 3 March 1998
Abstract Friction is a very important in¯uencing factor in metal forming. Especially during sheet metal forming, the surface of the workpiece has to be considered carefully in order to build up an adequate model for the numerical simulation of the whole forming process. Friction models implemented in most commercial Finite-element programs are usually based on the Coulomb- or Prandtl-model. Experimental identi®cation of the friction parameters for each interface material is needed. For the evolution of the surface structure during the contact phase, a micro-mechanical approach is necessary, but for practical reasons it cannot be obtained easily by measurements. In this work a new concept for the description of the surface structure is presented. The approach is based on the insertion of a ®ctive intermediate layer between the tool and an ideal roughnessless workpiece. The roughness of the real workpiece is represented by the porosity of the arti®cial intermediate layer. The constitutive behaviour of this intermediate material is modelled by a compressible material law. These laws are well known and are used mostly to describe damage mechanics. The initial value of the porosity can be ®xed by an ordinary measurement of the surface topography. The model is veri®ed by numerical and experimental investigations under different load modes in order to check the correctness of the assumptions. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Friction; Metal forming; Finite-element programs
1. Introduction The determination of friction phenomena is one of the most essential topics for the design of sheet metal forming processes. Especially for Finite-element simulation the development of innovative local friction laws will improve the quality of the numerical results. The surface of the sheet is one of the most important in¯uencing factors on friction because it transfers the forces between the tool and the workpiece. The applied forces, however, modify the surface structure, so it is clear that surface changes lead to different frictional behaviour also. Starting from this, many attempts have been made to determine and predict the surface changes in contact. One tries to perform these calculations
*Corresponding author. Tel.: +49-511-762-5550; fax: +49-511-7623007 E-mail address: [email protected] (C. Kaminsky)
in order to obtain a higher local resolution of the processes, which could have a great in¯uence on friction [1]. Recent developments in FEM analysis have established this technique as the principle technique for the simulation of metal forming processes in order to calculate stresses and strains in workpieces. Many authors have used this method to calculate the microscopic surface changes based on FE meshed pro®les, also, see e.g. [2] or [3]. However, there are numerous problems which let this kind of FEM application seem to be doubtful. First of all the discretisation of a surface is very dif®cult. In Fig. 1 a pro®le of a typical sheet metal surface is depicted. It can be observed easily that there are precipitous transitions between the roughness peaks and valleys. The meshing of such an object having a non-smooth edge leads to great dif®culties and becomes impossible for a real structure. To illustrate this, an idealised surface pro®le has been created to perform some studies. In Fig. 2 one can see this arti®cial pro®le. Compared with the original structure in
0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 9 9 ) 0 0 1 0 2 - 8
190
E. Doege et al. / Journal of Materials Processing Technology 94 (1999) 189±192
2. Introduction of an artificial intermediate layer
Fig. 1. A typical profile of a sheet metal surface.
Fig. 1 the simpli®cation is obvious. This pro®le is pushed down with a ¯at punch. It is shown that the material of the peaks ¯ows into the valleys. At the end of this forming process all of the asperities are leveled. One can see this behaviour in Fig. 2 where the calculated vertical displacement of the surface roughness is presented. The typical problem of this kind of calculation is that the mesh immediately degenerates because of the deformations of the roughness peaks. This has a great in¯uence on the convergence behaviour. Additionally, self-contact problems occur when the roughness valleys close. An extract of the idealised meshed surface pro®le is shown in Fig. 3. One can easily recognise how the elements distort and how they contact each other. The number of elements used is about 3000, and the computation time required is about 120 min. Therefore the simulation of a real 3D-structure forming process considering the surface changes is hardly possible at all, due to these formal dif®culties. Another problem is the commonly used constitutive laws. The elastic and plastic material parameters are only valid for a macroscopic scale. The single roughness asperities, however, have a microscopic scale in which the parameters have completely different magnitudes. In this area, the orientation of the peaks, the microscopic characteristics of each material point have to be considered and modelled. Unfortunately, this is possible only for relatively simple structures.
In order to take into account the microscopic behaviour of a physical phenomenon for a macromechanical calculation it is necessary to create a new state variable that associates the characteristics of the surrounding volume with the node of an FE model. This method is used commonly, e.g. for the description of failure mechanisms inside the material during deformation. One of the possibilities to describe the evolution of the surface roughness during the forming process is the introduction of an additional state variable that allows the consideration of the micromechanical behaviour of a macromechanical description. This approach follows a phenomenological pattern. For the computation of real forming processes it is absolutely necessary to stay within the borders of the continuum mechanics because commercial FEM programmes are based on a macro-mechanical theory. Conventionally the following parameters are used for the characterisation of technical surfaces: (i) centre line average height Ra; (ii) depth of roughness Rz; and (iii) and maximum pro®le height Ry. It is a matter of fact that only the initial values of roughness are used. Within a forming process the surface topography changes under the applied loads. Therefore the conventional description neglects these changes, which have a great in¯uence on phenomena such as friction, lubrication, and wear. For example, the size and shape of the lubrication pockets of deterministic produced sheets (Lasertex-sheets) are altered by contacting forces. The drawbacks of the macroscopic fracture criteria gave rise to the idea of applying the concepts of the mechanics of a compressible medium and damage mechanics [4] to describe the changing of the roughness as a change of damage variable, i.e. porosity. Computing the evolution of an average roughness with the measured initial value to the end of the forming process, damage mechanics bridges the ®eld of continuum mechanics dedicated to the study of perfectly homogeneous deformable bodies, and fracture mechanics, by describing the microscopic processes that
Fig. 2. Development of the displacement v.
E. Doege et al. / Journal of Materials Processing Technology 94 (1999) 189±192
191
Fig. 3. The problem of mesh degeneration.
precede ductile failure. One class of these models to account for internal damage is the following form: AJ2 BJ12 DY02 ;
(1)
where J20 is the second invariant of the deviatoric stress tensor; J1 the ®rst invariant of the stress tensor; and Y0 is the actual yield stress of the material. The parameters A, B and D are functions of the damage variable, i.e. porosity f, and their values can be found in literature [5,6]. For the present computations the following functions have been chosen: A 3; B
2:49f 0:514 2 and D 1 ÿ f 5 : 9
(2)
The values of the contact stress tensor are used in the nonlinear Eq. (1) to calculate the evolution of porosity during the simulation of the forming process. In the following model, the porosity f is associated with the average roughness height Ra. The functional form of the parameters A, B and D is to be veri®ed by advanced material tests. For present computations the functional dependence after [5] is assumed. It should be taken into account, that for deformable material the porosity has a three-dimensional characteristic, and Ra has a linear characteristic. Therefore, to compare these values, for an isotropic p material one has to operate with conjugate variables 3 f and Ra. For calculations, a statistically representative unit cell (unit length Lu) must be chosen, in the present study this being p equal to 1.18 mm. This unit cell adjusts the scaled porosity 3 f to the roughness Ra. 3. Experimental verification In order to check the assumptions, a process with a relative simple geometry is investigated. This can be seen in Fig. 4. On several sheet metal specimens (material St14, size 1001001 mm3) different loads are applied. The
Fig. 4. Experimental set-up for verification.
Table 1 Results of the experimental investigations Surface traction (N/mm2)
Ra (mm)
RZ (mm)
RY (mm)
0 100 150 200 250 300 350 400
0.94 0.94 0.84 0.80 0.80 0.69 0.67 0.56
5.28 5.10 4.61 4.34 4.32 3.91 4.00 3.46
6.63 6.36 5.45 5.26 5.02 4.63 4.74 4.19
punch used has a diameter of dp30 mm. Each sheet metal is loaded with a pre-de®ned force so that a controlled stress state occurs. In Table 1 the seven loading steps, the values of contact stress on each load step, and the measured values of roughness, can be seen. It is clear that the roughness decreases with increasing load because the asperities and peaks of the
192
E. Doege et al. / Journal of Materials Processing Technology 94 (1999) 189±192
Fig. 5. Decreasing roughness parameters with increasing load. Table 2 Results of experiment and numerical calculation of the scaled porosity p Surface traction 3 f dimensionless Ra/Lu (dimensionless) 2 (N/mm ) 100 150 200 250 300 350 400
0.80 0.71 0.68 0.68 0.58 0.57 0.47
0.80 0.75 0.70 0.65 0.60 0.54 0.46
surface are smoothed and leveled by the punch. The results are depicted graphically in Fig. 5. Ra pIn Table 2 the ratio Lu is compared to the computed value 3 f . It can be observed that the values for the measured p roughness RLua ®t to the computed values for the porosity 3 f very well. Thus it is possible to predict the mircrostructural changes of the surface roughness with a macroscopic law. In Fig. 6 the experimental and calculated data are presented graphically. Their comparison is very satisfactory. For every contact node of a FEM model a new variable can be calculated that represents the actual state of the surface for a given load history. 4. Conclusions The character of a surface has a great in¯uence on its frictional behaviour. Therefore it is important to ®nd a criterion that is able to describe the evolution of the surface under load adequately. The commonly used way is to simulate the surface and the material behaviour with the same Finite-element mesh. This has some disadvantages such as meshing a real surface topography, degenerating
Fig. 6. Comparison between experiment and simulation.
elements, self-contact and divergence of the solution. Additionally, for the simulation of real workpieces, the above approach is not appropriated because only small areas can be examined. It seems to be more suitable and physically justified to have macroscopic access, both for the macroscopic material behaviour and the microscopic surface changes. In damage mechanics and the mechanics of a compressible medium, e.g., this kind of combining of microand macro-methods is well known. This is why an artificial layer that is characterised by a so called scaled porosity analogously to the mechanics of a compressible medium is introduced here. As has been shown, the predicted porosity evolution fits the experimentally measured changes of the roughness under load. It may be concluded that the introduction of the concept of the artificial layer is a possibility in predicting the surface evolution. The FEM simulation of real sheet metal parts can be carried out, including these surface changes. References [1] B. Laackman, Beitrag zur fraktalen Beschreibung technischer OberflaÈchen, Dissertation, UniversitaÈt Hannover, 1996. [2] T. Neudecker, M. Pfestorf, U. Engel, EinglaÈttung strukturierter OberflaÈchen unter Druckbelastung mit und ohne Schmierstoffeinsatz, Proceedings of the Eighth Deutschsprachiges ABAQUS-Anwendertreffen, 30 September±1 October 1996, Hannover, Germany, pp. 11± 20. [3] R. BuÈnten, FEM-Modell zur Beschreibung von OberflaÈchenveraÈnderungen, Aufrauh- und ReibungsphaÈnomene im metallischen Kontakt, Dissertation, RWTH Aachen, 1996. [4] J. Lemaitre, A Course on Damage Mechanics, Springer, Berlin, 1992. [5] S.M. Doraivelu et al., A new yield function for compressible P/M materials, Int. J. Mech. Sci. 26(9±10) (1984) 527±535. [6] S. Shima, M. Oyane, Plasticity theory for porous metals, Int. J. Mech. Sci. 18 (1976) 285.
A new concept for the description of surface friction phenomena E. Doege, C. Kaminsky*, A. Bagaviev Institut fuÈr Umformtechnik und Umformmaschinen, UniversitaÈt Hannover, Welfengarten 1A, 30167 Hannover, Germany Accepted 3 March 1998
Abstract Friction is a very important in¯uencing factor in metal forming. Especially during sheet metal forming, the surface of the workpiece has to be considered carefully in order to build up an adequate model for the numerical simulation of the whole forming process. Friction models implemented in most commercial Finite-element programs are usually based on the Coulomb- or Prandtl-model. Experimental identi®cation of the friction parameters for each interface material is needed. For the evolution of the surface structure during the contact phase, a micro-mechanical approach is necessary, but for practical reasons it cannot be obtained easily by measurements. In this work a new concept for the description of the surface structure is presented. The approach is based on the insertion of a ®ctive intermediate layer between the tool and an ideal roughnessless workpiece. The roughness of the real workpiece is represented by the porosity of the arti®cial intermediate layer. The constitutive behaviour of this intermediate material is modelled by a compressible material law. These laws are well known and are used mostly to describe damage mechanics. The initial value of the porosity can be ®xed by an ordinary measurement of the surface topography. The model is veri®ed by numerical and experimental investigations under different load modes in order to check the correctness of the assumptions. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Friction; Metal forming; Finite-element programs
1. Introduction The determination of friction phenomena is one of the most essential topics for the design of sheet metal forming processes. Especially for Finite-element simulation the development of innovative local friction laws will improve the quality of the numerical results. The surface of the sheet is one of the most important in¯uencing factors on friction because it transfers the forces between the tool and the workpiece. The applied forces, however, modify the surface structure, so it is clear that surface changes lead to different frictional behaviour also. Starting from this, many attempts have been made to determine and predict the surface changes in contact. One tries to perform these calculations
*Corresponding author. Tel.: +49-511-762-5550; fax: +49-511-7623007 E-mail address: [email protected] (C. Kaminsky)
in order to obtain a higher local resolution of the processes, which could have a great in¯uence on friction [1]. Recent developments in FEM analysis have established this technique as the principle technique for the simulation of metal forming processes in order to calculate stresses and strains in workpieces. Many authors have used this method to calculate the microscopic surface changes based on FE meshed pro®les, also, see e.g. [2] or [3]. However, there are numerous problems which let this kind of FEM application seem to be doubtful. First of all the discretisation of a surface is very dif®cult. In Fig. 1 a pro®le of a typical sheet metal surface is depicted. It can be observed easily that there are precipitous transitions between the roughness peaks and valleys. The meshing of such an object having a non-smooth edge leads to great dif®culties and becomes impossible for a real structure. To illustrate this, an idealised surface pro®le has been created to perform some studies. In Fig. 2 one can see this arti®cial pro®le. Compared with the original structure in
0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 9 9 ) 0 0 1 0 2 - 8
190
E. Doege et al. / Journal of Materials Processing Technology 94 (1999) 189±192
2. Introduction of an artificial intermediate layer
Fig. 1. A typical profile of a sheet metal surface.
Fig. 1 the simpli®cation is obvious. This pro®le is pushed down with a ¯at punch. It is shown that the material of the peaks ¯ows into the valleys. At the end of this forming process all of the asperities are leveled. One can see this behaviour in Fig. 2 where the calculated vertical displacement of the surface roughness is presented. The typical problem of this kind of calculation is that the mesh immediately degenerates because of the deformations of the roughness peaks. This has a great in¯uence on the convergence behaviour. Additionally, self-contact problems occur when the roughness valleys close. An extract of the idealised meshed surface pro®le is shown in Fig. 3. One can easily recognise how the elements distort and how they contact each other. The number of elements used is about 3000, and the computation time required is about 120 min. Therefore the simulation of a real 3D-structure forming process considering the surface changes is hardly possible at all, due to these formal dif®culties. Another problem is the commonly used constitutive laws. The elastic and plastic material parameters are only valid for a macroscopic scale. The single roughness asperities, however, have a microscopic scale in which the parameters have completely different magnitudes. In this area, the orientation of the peaks, the microscopic characteristics of each material point have to be considered and modelled. Unfortunately, this is possible only for relatively simple structures.
In order to take into account the microscopic behaviour of a physical phenomenon for a macromechanical calculation it is necessary to create a new state variable that associates the characteristics of the surrounding volume with the node of an FE model. This method is used commonly, e.g. for the description of failure mechanisms inside the material during deformation. One of the possibilities to describe the evolution of the surface roughness during the forming process is the introduction of an additional state variable that allows the consideration of the micromechanical behaviour of a macromechanical description. This approach follows a phenomenological pattern. For the computation of real forming processes it is absolutely necessary to stay within the borders of the continuum mechanics because commercial FEM programmes are based on a macro-mechanical theory. Conventionally the following parameters are used for the characterisation of technical surfaces: (i) centre line average height Ra; (ii) depth of roughness Rz; and (iii) and maximum pro®le height Ry. It is a matter of fact that only the initial values of roughness are used. Within a forming process the surface topography changes under the applied loads. Therefore the conventional description neglects these changes, which have a great in¯uence on phenomena such as friction, lubrication, and wear. For example, the size and shape of the lubrication pockets of deterministic produced sheets (Lasertex-sheets) are altered by contacting forces. The drawbacks of the macroscopic fracture criteria gave rise to the idea of applying the concepts of the mechanics of a compressible medium and damage mechanics [4] to describe the changing of the roughness as a change of damage variable, i.e. porosity. Computing the evolution of an average roughness with the measured initial value to the end of the forming process, damage mechanics bridges the ®eld of continuum mechanics dedicated to the study of perfectly homogeneous deformable bodies, and fracture mechanics, by describing the microscopic processes that
Fig. 2. Development of the displacement v.
E. Doege et al. / Journal of Materials Processing Technology 94 (1999) 189±192
191
Fig. 3. The problem of mesh degeneration.
precede ductile failure. One class of these models to account for internal damage is the following form: AJ2 BJ12 DY02 ;
(1)
where J20 is the second invariant of the deviatoric stress tensor; J1 the ®rst invariant of the stress tensor; and Y0 is the actual yield stress of the material. The parameters A, B and D are functions of the damage variable, i.e. porosity f, and their values can be found in literature [5,6]. For the present computations the following functions have been chosen: A 3; B
2:49f 0:514 2 and D 1 ÿ f 5 : 9
(2)
The values of the contact stress tensor are used in the nonlinear Eq. (1) to calculate the evolution of porosity during the simulation of the forming process. In the following model, the porosity f is associated with the average roughness height Ra. The functional form of the parameters A, B and D is to be veri®ed by advanced material tests. For present computations the functional dependence after [5] is assumed. It should be taken into account, that for deformable material the porosity has a three-dimensional characteristic, and Ra has a linear characteristic. Therefore, to compare these values, for an isotropic p material one has to operate with conjugate variables 3 f and Ra. For calculations, a statistically representative unit cell (unit length Lu) must be chosen, in the present study this being p equal to 1.18 mm. This unit cell adjusts the scaled porosity 3 f to the roughness Ra. 3. Experimental verification In order to check the assumptions, a process with a relative simple geometry is investigated. This can be seen in Fig. 4. On several sheet metal specimens (material St14, size 1001001 mm3) different loads are applied. The
Fig. 4. Experimental set-up for verification.
Table 1 Results of the experimental investigations Surface traction (N/mm2)
Ra (mm)
RZ (mm)
RY (mm)
0 100 150 200 250 300 350 400
0.94 0.94 0.84 0.80 0.80 0.69 0.67 0.56
5.28 5.10 4.61 4.34 4.32 3.91 4.00 3.46
6.63 6.36 5.45 5.26 5.02 4.63 4.74 4.19
punch used has a diameter of dp30 mm. Each sheet metal is loaded with a pre-de®ned force so that a controlled stress state occurs. In Table 1 the seven loading steps, the values of contact stress on each load step, and the measured values of roughness, can be seen. It is clear that the roughness decreases with increasing load because the asperities and peaks of the
192
E. Doege et al. / Journal of Materials Processing Technology 94 (1999) 189±192
Fig. 5. Decreasing roughness parameters with increasing load. Table 2 Results of experiment and numerical calculation of the scaled porosity p Surface traction 3 f dimensionless Ra/Lu (dimensionless) 2 (N/mm ) 100 150 200 250 300 350 400
0.80 0.71 0.68 0.68 0.58 0.57 0.47
0.80 0.75 0.70 0.65 0.60 0.54 0.46
surface are smoothed and leveled by the punch. The results are depicted graphically in Fig. 5. Ra pIn Table 2 the ratio Lu is compared to the computed value 3 f . It can be observed that the values for the measured p roughness RLua ®t to the computed values for the porosity 3 f very well. Thus it is possible to predict the mircrostructural changes of the surface roughness with a macroscopic law. In Fig. 6 the experimental and calculated data are presented graphically. Their comparison is very satisfactory. For every contact node of a FEM model a new variable can be calculated that represents the actual state of the surface for a given load history. 4. Conclusions The character of a surface has a great in¯uence on its frictional behaviour. Therefore it is important to ®nd a criterion that is able to describe the evolution of the surface under load adequately. The commonly used way is to simulate the surface and the material behaviour with the same Finite-element mesh. This has some disadvantages such as meshing a real surface topography, degenerating
Fig. 6. Comparison between experiment and simulation.
elements, self-contact and divergence of the solution. Additionally, for the simulation of real workpieces, the above approach is not appropriated because only small areas can be examined. It seems to be more suitable and physically justified to have macroscopic access, both for the macroscopic material behaviour and the microscopic surface changes. In damage mechanics and the mechanics of a compressible medium, e.g., this kind of combining of microand macro-methods is well known. This is why an artificial layer that is characterised by a so called scaled porosity analogously to the mechanics of a compressible medium is introduced here. As has been shown, the predicted porosity evolution fits the experimentally measured changes of the roughness under load. It may be concluded that the introduction of the concept of the artificial layer is a possibility in predicting the surface evolution. The FEM simulation of real sheet metal parts can be carried out, including these surface changes. References [1] B. Laackman, Beitrag zur fraktalen Beschreibung technischer OberflaÈchen, Dissertation, UniversitaÈt Hannover, 1996. [2] T. Neudecker, M. Pfestorf, U. Engel, EinglaÈttung strukturierter OberflaÈchen unter Druckbelastung mit und ohne Schmierstoffeinsatz, Proceedings of the Eighth Deutschsprachiges ABAQUS-Anwendertreffen, 30 September±1 October 1996, Hannover, Germany, pp. 11± 20. [3] R. BuÈnten, FEM-Modell zur Beschreibung von OberflaÈchenveraÈnderungen, Aufrauh- und ReibungsphaÈnomene im metallischen Kontakt, Dissertation, RWTH Aachen, 1996. [4] J. Lemaitre, A Course on Damage Mechanics, Springer, Berlin, 1992. [5] S.M. Doraivelu et al., A new yield function for compressible P/M materials, Int. J. Mech. Sci. 26(9±10) (1984) 527±535. [6] S. Shima, M. Oyane, Plasticity theory for porous metals, Int. J. Mech. Sci. 18 (1976) 285.