Tensile Decohesion by Local Failure Criteria

Transcription

1 TCHNSCH MCHANK, Band S, Heft 4, (1998), Manuskripeingang. 19. Dezembcr 1997 Tensie Decohesion by Loca Faiure Criteria T. Siegmund, W. Brocks Debonding of two eastic-pastic bocks by a ductie faiure mechanism is investigated. The bond ine between the two bocks is specified either as a strip of a materia described by the modified Gurson reation or by a cohesive zone mode. The cohesive zone materia parameters are deduced from anayses of void containing unit ces apart from the debonding anaysis. Here, the behavior of the materia is described by the modified Gurson mode. The present computations of debonding show that the externa stress biarciaity imposed on a specimen has important impications on the agreement between the predictions of the two modes. At high eve of externa stress biariaity the predicted debonding behavior is influenced itte by changes in the oading conditions. The cohesive zone parameters as deduced from uniaria straining ead to good agreement with the predictions of the Gurson mode. At ow eves of appied stress biaviaity the debonding behavior is strongy dependent on a change in externa oading and an a priori choice of cohesive materia parameters was not possibe, 1 ntroduction An essentia ingredient of materia modeing aimed to characterize materia faiure is that the constitu tive description of the materia under consideration has to aow that the deformation ocaizes or that the materia can ose its capacity to transmit stresses. f materia faiure is due to ductie tearing i.e. induced by void growth and void coaescence there exist two approaches to the modeing of materia separation. n both approaches the zone where materia degradation takes pace is termed process zone which is embedded in a materia that does not fai. One approach that can mirror the oca oss of stress carrying capacity is the introduction of a cohesive zone where the tractions in the process zone are reated to the magnitude of materia separation. Such a type of a traction separation aw has been introduced by Barenbatt (1962) and possesses mainy two materia parameters, a cohesive strength and a cohesive energy. This mode has become attractive again recenty for a series of appications in the computationa modeing of fracture. Appications of cohe sive modes to ductie fracture incude the simuation of quasistatic oading, Needeman (1990a,1990b), Tvergaard et a. (1992, 1994, 1996), Yuan et a. (1996), Siegmund et a. (1997) and dynamic oading, Siegmund et a. (1997), as we as the appication to bimateria systems, Siegmund et a. (1997), and composite materias, Needeman (1987), Tvergaard (1993), Finot et a. (1994). These appications demon strate that the trends predicted by the appication of a cohesive zone mode are quite sensitive to the choice of the cohesive zone parameters. Ony reativey sma changes in the parameter vaues may resut in a strong variation of the predicted specimen response. An aternative way for the anaysis of crack growth is the use of the Gurson constitutive equation and its modification, Needeman et a. (1984). This approach incorporates severa of the physica detais of the micromechanisms of faiure into the materia s constitutive equation: this is an initia void voume fraction, void nuceation and growth, as we as fina void coaescence. This approach has successfuy been appied by numerous authors, e.g. Needeman et a. (1987), Sun et a. (1992), Brocks et a. (1995), Xia et a. (1995), Ruggieri et a. (1997), to investigate the propagation of cracks in ductie materias in various specimen geometries. The recent work of Xia et a. (1995) and Ruggieri et a. (1997) demon strate an interesting approach on how this constitutive equation can easiy be connected with a mi crostructura ength scae. n the first part of the paper the cohesive zone materia parameters are determined by the use of the modified Gurson constitutive equation. Specia consideration is given to the influence of the triaxiaity of the stress state on the cohesive materia parameters. n the second part the probem of decohesion of two bocks is anayzed, Needeman (1990a,1990b). The geometry of the specimen under investigation is depicted in Figure 1a. The process zone bonding the two bocks together is described in two different ways, see Figure 1b: (1) by the use of a cohesive zone mode and (2) by the use of the modified Gurson constitutive equation. Here, the materia parameters 261

2 for the cohesive mode are deduced from the mode materia used in Both modes have in common that a ength scae is introduced into the cacuation and that the stresses in the process zone are imited in their magnitude. (1) Cohesive Zone Mode tie run; ( n un Figure 1... (2) Gurson Mode astc-pastc hydrostatic stress A +22 L f=0.0 f>0 (a) (b) effective stress (a) The Specimen under Consideration. The Bonding Region of Height D is the Region in which Materia Faiure is Aowed to Occur. (b) Visuaization of the Two Approaches Used for the Description of the Bonding Region: (1) the Cohesive Zone Mode and (2) the Gurson Mode Having in mind that both modes are intended as predictive toos in computationa fracture mechanics it is the intention of this investigation to compare the cacuated behavior of the two approaches. Limitations of the appicabiity of the two modes are sought. 2 The Cohesive Zone Parameters The separation of two materia bocks aong a predefined process zone can be described by use of a cohesive zone mode. The present study uses the traction separation reation of Needeman (1990a). This mode is shorty reintroduced in the foowing. The simuation of pure mode crack growth is considered and ony norma separation aong the assumed crack path occurs. The traction dispacement reation (Figure 2) then reads: 0'n = amaxe - zu n exp ( 2351) (1) 6 6 Here, an is the norma traction at the crack pane and un is the dispacement jump across the crack, i.e. the crack tip opening dispacement. z = 16e/9 and e : exp(1). 6 is the characteristic ength of the cohesive zone mode and am is the maximum vaue that is reached by on. The cohesive energy,, for this traction dispacement reation equas 9 r gmarö For the present formuation the main portion of energy is spent between un : 0 and un : 6. t now 262

3 remains to determine two of the cohesive materia parameters, either am, or 6, for the materia under consideration. «Sn/csmax 2.0 Figure 2. The Traction Separation Law Used With reference to Tvergaard et a. (1992) the modified Gurson mode, see e.g. Needeman et a1. (1984), is used to predict the traction-dispacement aw for a materia that fais by the growth of voids and coaescence of voids. A materia eement of size D X D is taken out of the process zone. This materia eement is anayzed in pane strain under a homogeneous stress strain state. The yied function of the modified Gurson reation used in the present context is 2 Ö : (001:!) +2q1f* cosh ( 31%) - [1+9]3 (f*)2] : 0 (3) Here, 0'8, is the von Mises stress and oh the hydrostatic stress acting on the materia ce. (7M is the fow strength of the materia surrounding the void. The uniaxia strain stress response of the eastic-pastic materia that surrounds the void is described by e z a/ for a S 00 (4) e z (Jg/)(U/cro)(1/N) for 0' 2 0'0 (5) where, 0'0,N denote eastic moduus, yied strength of the materia and strain hardening coefficient, respectivey. The materia properties are taken to be /O o : 500 and N : 0.1. Poisson s ratio is u = 0.3. The vaues of the parameters, q1,q2,q3, used for the modified Gurson reation are q1 = 1.5, q; = 1.0, q3 = qä. The effect of void coaescence and fina oss of stress carrying capacity is captured by using the modified voume fraction, f". Here, f* (f) is taken as a biinear function of f: f* (f) = f for f S f0 and f" (f) = fa + k(f fa) for f > fa. Fina faiure occurs if the condition f* (ff) : 1/q1 is reached. n the foowing attention is focussed on preexisting voids ony. A cacuations were performed for f0 : 0.005,fc : 0.15, k : n one set of cacuations the oading of the ce is performed under various constant overa true stress ratios, p, see Figure 3a, U1 P: (6) 02 Furthermore, the boundaries of the ce remain straight and parae to their initia configuration. For pane strain and incompressibe materia behavior the stress ratio, p, prescribed to the computationa 263

4 ce is reated to the triaxiaity, T, by _11+p (U The behavior of the materia ce was investigated for appied stress ratios p 20.27, 0.44, 0.55, 0.68, 0.75, These vaues correspond to appied stress triaxiaities of T 21.0, 1.5, 2.0, 3.0, 4.0, 5.0. An additiona cacuation was performed for the condition of uniaxia straining, Figure 3b. This boundary condition is the same as used in Tvergaard et a1. (1992) for the determination of the materia parameters for their cohesive zone mode. < O '1 > (a) 02 (b) 02 Figure 3. The Unit Ce Set up. (a) Constant Appied Stress Ratio, (b) Uniaxia Straining The oading under constant prescribed stress ratio, p, is performed using the modified Riks method as impemented in the finite eement code ABAQUS, H.K.S. nc. (1997). One singe four node pane strain eement was taken to represent the materia ce. The modified Gurson constitutive reation was impemented into a UMAT subroutine for the finite eement code ABAQUS using the method as proposed by Aravas (1987) and Zhang (1994). 3 Determination of Parameter Vaues Figure 4 depicts the resuts of the cacuations of the behavior of a ce under various stress ratios and uniaxia straining, respectivey. Attention is focused on the materia traction separation response in the main oading direction, parae to 0 2. n a cases as the dispacement increases the traction goes through a maximum vaue and a subsequent reduction in stress carrying capacity is found. The stage of fina oss of oad carrying capacity associated with the mechanisms of void coaescence as captured by the modified Gurson mode is reached at the knee of the traction separation curves. The maximum traction vaues of the curves in Figure 4 are identified with the cohesive strength, am. The cohesive strength increases nonineary as the appied triaxiaity is increased. At high vaues of T the cohesive strength as predicted for the boundary conditions of constant appied stress ratio approaches the vaue predicted for the uniaxia straining boundary conditions. The work of separation, i.e. the vaues of the integra 'ep WZ/ 2 Ugd üg 0 are depicted in Figure 5. The imiting vaues of this integra after fina separation is identified with the cohesive energy, F. The vaues of the cohesive energy F/(oo D) again depend on T. The vaues of F/(oo D) decrease with increasing appied stress triaxiaities. At high appied triaxiaities F is sighty smaer than the vaue obtained for the boundary conditions of uniaxia straining. The vaue of the uniaxia straining case is we described by Tvergaard et a. (1992): 1 rzimp (9 The oading history under imposed uniaxia straining is distincty different from that under constant imposed stress ratio. t is worth noting the fact, that despite the strongy different oading histories 264

5 present in the uniaxia case and for T : 4.0 and 5.0 the predicted vaues of am and F differ ony sighty from the vaues determined for the uniaxia straining case. 62/60 Figure 4. The Traction Separation Behavior of a Unit Ce Described by the Modified Gurson Reation under Various Constant Appied Stress Ratios and Uniaxia Straining ,.,'w T=1_0 _..-.._. Ti ) p ' """ -- T= T=4.0 _.._.. T=2,0 _..... T250 ' 1:0, X1=L _ A no 10 _ b ä [ _ uz/d Figure 5. The voution of the Work of Separation for the Traction Separation Curves in Figure 4 for Various Appied Stress Triaxiaities and Uniaxia Straining From the resuts presented in Figs. 4 and 5 three sets of cohesive zone properties are taken for further considerations; data are taken from oading with T : 20,30 and from the case of uniaxia straining, CZM#2, CZM#3, OZ M#uni. These sets of cohesive materia properties are summarized in Tabe 1. The cohesive characteristic engths, Ö, is cacuated from the vaues of the cohesive strengths and the cohesive energies by using equation Name of data set Umaz/O'o 6/D F/(O'OD) CZM# CZM# CZM#uni Tabe 1. The Materia Data Used in the Cacuations n a the foowing considerations the differences in shape of the traction separation curves as depicted in Figure 2 and Figure 4 are disregarded in the determination of the cohesive zone materia parameters. 265

6 4 Debonding of Two astic-pastic Bocks The mode probem used in the present investigation is the decohesion of two bocks of an eastic-pastic materia bonded together without any imperfections. The geometry of the specimen under investigation is depicted in Figure 1a. The specimen possesses the dimension 2L x 2L and is deformed under conditions of pane strain. The specimen is ocated in the x1~z2 pane and is assumed to have unit thickness. Symmetry conditions are assumed to prevai and ony one quadrant of the specimen is anayzed. The boundary conditions imposed in terms of the boundary dispacements, U1, U2, and the tractions, 71,72, on the quadrant 1:1 > 0 and $2 > 0 are: U1 : 0 and 72 : 0 on x1 = 0 (10) ug = 0 and 71 = 0 on x2 = 0 (11) u : U1 and 72 : 0 on 1:1 : L (12) uz : U2 and on wg = L (13) T1 = 0 Loading again is performed under constant appied stress ratios, p, equation (6). Now Lei-U; L+U2/O 1 2 z L+U1/0 Td 1 $2 at $1 = L ( 14 ) T2d$2 a t $2 : L ( 15) L+Ug For oading under uniaxia straining, U1 2 O. The oading under constant stress ratio was again achieved using the modified Riks method, keeping the ratio 21/22 constant. n the approach using the modified Gurson equation a singe row of void containing ces represents the process zone aong the re-axis. Due to the symmetry conditions a row of 20 quadriatera eements of initia height D/2 represent the process zone. The materia data used for the description of the process zone in the debonding study are identica to those stated in the previous section. The materia surrounding the region of void containing ces is a non damageabe eastic pastic materia foowing a Jg pasticity theory. ts materia properties are taken to be identica with those of the matrix materia surrounding the voids in the ce mode study. The uniaxia straining properties are given in equation A uniformy spaced mesh region with 40 X 39 equa sized quadriatera eements is used in the remainder of the quadrant anayzed. The ratio between the process zone height (D) and the overa specimen dimension L was taken to be L/ D = 100. n the presentation of the computationa resuts the curves obtained with process zone modeed by the modified Gurson reation are marked GTN. The aternative approach used is the substitution of the row of void containing ces by a series of cohesive eements. The mode contains 40 X 39 continuum eements with eastic-pastic materia properties (equation and 40 cohesive eements at the x axes. The cohesive eements used in the present cacuation possess two integration points. The impementation of the cohesive eements in the finite eement code ABAQUS, H.K.S. nc. (1997) was performed by the use of user defined eements (UL) in ine with the theory stated in Needeman (1987). Again assuming L/ D = 100 the size of the specimen, L, reative to the cohesive characteristic ength, 6 is L/62159, 275, 538 for CZM#2 CZM#3, CZM#uni respectivey. 5 Resuts Decohesion under monotonic oading of the specimen in Figure 1a was cacuated for appied constant stress ratios of p 2: 0.44, 0.55, 0.67 and uniaxia straining. n fracture mechanics the term constraint, i.e. the restriction of deformation, is often used to quantify the conditions under which materia faiure takes pace. For exampe, an increase in p is equivaent to an increase in constraint. The present simuations of debonding were performed with the aim to see if different descriptions of the process zone can reflect a change in oading conditions in a simiar way. For each vaue of appied stress ratio the process zone was modeed both using the ce mode with the materia data given in the previous section 266

7 and the cohesive zone mode with the materia data sets CZM#2, CZM#3, CZM#uni. Resuts of the computed overa specimen behavior are depicted in the form of curves of true stress, 22, vs. ogarithmic strain, 2 z n((u2 + L) /L). Figures 6 a to d depict this resuts in the order of decreasing stress ratio. n ine with the resuts pubished by Needeman (1990a,1990b) it is observed that at high appied stress ratios the debonding process takes pace at ow overa deformation, Figure 6a,b. The goba specimen behavior for uniaxia straining and p = 0.67 as predicted by the use of the modified Gurson reation are in very good agreement with the behavior as predicted by the use of the data set C'ZM#uni in the cohesive zone eements. The use of both other data sets, CZM#2, CZM#3, eads to ower maximum P o o b \ x! 3:524,../:--', / _ 7 1' GTN.Lij - CZM#2 _ g; _- CZM#2.'.s' CZM#3 A; -- - CZM#3.-.55" --- CZM#um. ' --- CZM#uni "L _2 (a) ' _2 0_O _.-" 5'10. o 4,3! : H _3' N \ ' r g ' ; " 20 N j/ x. 3,t ;:.z' "i. N 1.-"'/' N N O p. o vaues of the goba stress due to the ower cohesive strengths in these data sets.. 0 -_- GTN 1-. ~~ (b) Tr, ":. N ' N 2.0 f ' : 5 g ; :t - M. GTN : - CZM#2 - : _... CZM#3 \.. S (C) 2 O (d) Figure 6. Overa Stress Strain Curves for Various Loading Situations and Process Zone Descrip tions; (a) Uniaxia Straining, (b) p = 0.66, (c) p = 0.55, and (d) p = 0.44 The debonding behavior changes consideraby when the appied stress ratio is decreased. Two simuations of debonding at ow vaues of p are depicted in Figure 6c and d, for p = 0.55 and p z: 0.44, respectivey. t is worth noting the change in the scae of the strain axis. For p = 0.55 and p = 0.44 debonding occurs ony after considerabe deformation of the bocks has taken pace. The good agreement between the debonding behavior as predicted by the modified Gurson equation and the use of CZM#uni is ost at these stress ratios. t is found that for p = 0.55 it is the use of data set CZM#3 that predicts the debonding in good agreement with the predictions of the modified Gurson mode, whie for p = 0.44 it is the data set CZM#2. For both these two cases the use of the data set CZM#uni argey overestimates the strains to faiure. Figure 7 depicts the oading unoading of a point within the bock materia, again in the order of increasing stress ratio. The trends in the agreement aready observed from Figure 6 are mirrored in Figure 7 in the same way. The oading behavior of a point outside the process zone is again very strongy influenced by the appied stress ratio. Thus, for the approach using the Gurson mode the strain to faiure depends strongy on p. For the cohesive zone mode the predicted faiure behavior again strongy depends on the choice of the data set. 267

8 4.0 ' O 1 b / f \N 4" bn, "i / i! um. GTN,' /" ; -._- CZM#2,'. 1 GTN _._... CZM#3 / -- CZM#2 _.._ CZMguni,' ---CZM#3 O O, "1/. "_ 1~1o~ ' 0 5' (b) "5 ~ :.' s i : ' : i N ' = : 1 - N.' : _ b2.0 ~! -.= ' Z : ä g m- GTN 5 g. mm GTN i g g CZM#2 i : g : i _... CZM#3 ; g : CZM#unii. u o ~100 (d) 22 Figure 7. Stress Strain Curves for a Materia Point Outside of the Process Zone for Various Loading Situations and Process Zone Descriptions; (a) Uniaxia Straining, (b) p = 0.66, (c) p = 0.55, (d) p z 0.44 Figure 8. Stress Strah Curves of a Materia Point nside the Process Zone for Various Loading Situations and Process Zone Descriptions Whie the amount of deformation for a point outside the process zone depends strongy on the appied stress ratio this is not the case for the process zone. The oading unoading behavior of a materia point within the process zone is now depicted in Figure 8. The traction separation curves for the cohesive zone mode are independent of p whie the traction separation curves for the modified Gurson mode are definitey dependent on the appied stress ratio. The traction separation curves for the uniaxia straining and the case of p : 0.67 are neary identica despite the difference in the oading history. The maximum stress reached in that case is identica with the cohesive strength in materia data set CZM#uni. A reduction in p resuts in a reduction of the maximum of the stress for the process zone modeed by the modified Gurson reation. For p = 0.55 the maximum vaue equas the cohesive strength in data 268

9 set CZM#3 and for p = 0.44 for data set CZM#2, respectivey. Again, the shapes of the traction separation curves are different for the two descriptions of the process zone but this apparenty has a minor influence on the overa debonding behavior. 6 Concusion The debonding behavior of two bocks made of an isotropic eastic-pastic materia was anayzed by the two distincty different approaches of the modified Gurson reation and a cohesive zone mode. n the first part of the paper it is shown that in the determination of the cohesive zone parameters specia attention has to be devoted to the boundary conditions. The resuting cohesive zone parameters are strongy dependent on the oading conditions as quantified by the parameter stress ratio, p. Thus, it is necessary to test if there exists a set of materia data that can describe the debonding of two bocks equay we under a oading situations appied to the bocks. The present investigation demonstrates that it is not possibe to choose a set of cohesive surface data that fufis these requirements. Ony for high biaxia oading situations the use of cohesive zone data derived from the ce under uniaxia straining provides an exceent choice. Here one finds good agreement between the resuting overa specimen behavior using the modified Gurson mode and the cohesive zone. This hods true even though the shape of the traction separation curves as predicted by the two modes are quite different. The dependence of the faiure behavior on the oading conditions becomes very arge at ow appied stress ratios, i.e. in the case where pastic deformation pays a arge roe. n that case no unique choice for the cohesive zone parameters can be made to obtain a fit with the predictions from the Gurson mode. n that regime the separation behavior as predicted by the Gurson mode becomes dependent on the appied stress ratio. That behavior cannot be foowed by the present version of the cohesive zone mode. Since the behavior of the process zone triggers the overa specimen behavior ony rather sma changes in the materia separation resut in arge changes in the overa specimen behavior, mainy the strain to faiure. Finay, it shoud be pointed out here that for the choice of the cohesive zone parameters even fufiing the condition of equa appied stress ratio in the ce mode and the decohesion probem does not resut in a good agreement between predictions from the cohesive zone mode and the modified Gurson mode, respectivey. Literature 1. ABAQUS, Version 5.6., H.K.S. nc., Pawtucket, U.S.A., (1997). 2. Aravas, N.: On the numerica integration of a cass of pressure-dependent pasticity modes, nt. J. Num. Meth. ngng, 24, (1987), Barenbatt G..: The mathematica theory of equiibrium cracks in britte fracture, Adv. App. Mech., 7, (1962), Brocks, W., Sun, D. Z., Honig, A.: Verification of the transferabiity of micromechanica parameters by ce mode cacuations with visco pastic materias, nt. J. Pasticity, 11, 8, (1995), Brocks, W., Kingbei, D., Kiinecke, Sun, D.-Z.: Appication of the Gurson mode to ductie tearing resistance, in: Constraint effects in fracture: Theory and appications, ASTM STP 144, Kirk, M., Bakker, A., (eds), Phiadephia, American Society for Testing and Materias, (1995), Finot, M., Shen, Y.-L., Needeman, A., Suresh, S.: Micromechanica modeing of reinforcement fracture in partice-reinforced meta matrix composites, Meta. Mater. Trans. A, 25, (1994), Hancock, J.W., Cowing, M.J.: Roe of state of stress in crack tip faiure processes, Meta Science, (1980), Kopik, J., Needeman, A.: Void growth and coaescence in porous pastic soids, nt. J. Soids Structures, 24, (1988), Yuan, H., Lin, G., Cornec, A.: Verification of a cohesive zone mode for ductie fracture, J. ng. Mater. Tech, 118, (1996), Needeman, A., Tvergaard, V.: An anaysis of ductie rupture in notched bars, J. Mech. Phys. Soids, 32, (1984),

10 Needeman, A.: A continuum mode for void nuceation by incusion debonding, J. App. 54, (1987) Mech., Needeman, A., Tvergaard, V.: An anaysis of ductie rupture modes at a crack tip, J. Mech. Phys. Soids, 35, (1987), Needeman, A.: An anaysis of decohesion aong an imperfect interface, nt. J. Fracture, 42, (1990a), Needeman, A.: An anaysis of tensie decohesion aong an interface, J. Mech. Phys. Soids, 38, (1990b), Ruggieri, C. Dodds, R.H., Panontin, T.L.: Numerica modeing of ductie crack growth in 3 D using computationa ce eements, nt. J. Fracture, 82, 1, (1997), Siegmund, T. Brocks, W.: Prediction of the work of separation in ductie fracture and impication to the modeing of ductie faiure, nt. J. Fracture, in print (1998). Siegmund, T., Needeman, A.: A numerica study of dynamic crack growth in eastic viscopastic soids, nt. J. Soids Structures, 34, 7, (1997), Siegmund, T. Needeman, A., Feck, N.A.: Dynamic Crack Growth Across an nterface, nt. J. Fracture, 85 (1997) Sun, D. Z.; Kienzer, R.; Voss, B.; Schmitt, W.: Appication of micromechanica modes to the prediction of ductie fracture, in: Fracture mechanics: Twenty-second Symposium (Vo. ), ASTM STP 1131, Newman, J.C., Jr., Raju,.S., pstein, J.S., (eds.) (1992), Tvergaard, V.; Hutchinson, J.W.: The reation between crack growth resistance and fracture process parameters in eastic pastic soids, J. Mech. Phys. Soids, 40, 6, (1992), Tvergaard, V.; Hutchinson, J.W.: ffect of T stress on mode crack growth resistance in a ductie soid, nt. J. Soids Structures, 31, 20-22, (1994), Tvergaard, V.; Hutchinson, J.W.: ffect of strain dependent cohesive zone mode on predictions of crack growth resistance, nt. J. Soids Structures, 33, 20-22, (1996), Tvergaard, V.: Mode studies of fibre breakage and debonding in a meta reinforced by short fibres, J. Mech. Phys. Soids, 41, (1993), Xia, L., Shih, C.F.: Ductie crack growth. A numerica study using computationa ces with microstructuray based ength scaes, J. Mech. Phys. Soids, 43, 2, (1995), Xia, L., Shih, C.F.: Ductie crack growth. Void nuceation and geometry effects on macroscopic fracture behavior, J. Mech. Phys. Soids, 43, 12, (1995), Zhang, Z.: Ph-D thesis, Norwegian University of Science and Technoogy, Trondheim, (1994). Address: Dr. Thomas Siegmund and Prof. Dr.-ng. Wofgang Brocks, nstitut fiir Werkstofforschung, GKSS-Forschungszentrum, D Geesthacht 270