Strain. Residual stresses in a Cu-CFC component for thermonuclear application: numerical prediction and experimental evaluation by indentation test

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1 Strain Residual stresses in a Cu-CFC component for thermonuclear application: numerical prediction and experimental evaluation by indentation test Journal: Strain Manuscript ID: STRAIN-0.R Manuscript Type: Full Paper Date Submitted by the Author: 0-Mar-00 Complete List of Authors: Bolzon, Gabriella; Politecnico di Milano, Department of Structural Engineering Chiarullo, Enzo; Politecnico di Milano, Department of Structural Engineering Casalegno, Valentina; Politecnico di Torino, Department of Materials Science and Chemical Engineering Salvo, Milena; Politecnico di Torino, Department of Materials Science and Chemical Engineering Keywords: Cu-CFC joints, residual stresses, indentation test, inverse analysis

2 Page of Strain 0 0 Residual stresses in a Cu-CFC component for thermonuclear application: numerical prediction and experimental evaluation by indentation test G. Bolzon, E.J. Chiarullo, V. Casalegno, M. Salvo Department of Structural Engineering, Politecnico di Milano, piazza Leonardo da Vinci, 0 Milano, Italy Department of Materials Science and Chemical Engineering, Politecnico di Torino, corso Duca degli Abruzzi, 0 Torino, Italy corresponding author: gabriella.bolzon@polimi.it; tel ; fax Abstract The present work concerns the assessment of residual stresses (RS) in a component for thermonuclear applications, made by the casting of copper on a carbon-fibre reinforced carbon composite and intended to be subjected to severe cycles of thermal, mechanical and neutron loads. The magnitude of RS left at the interface between the two materials in the production process, due to thermal expansion mismatch, has to be carefully assessed. In the present investigation, the likely spatial distribution of the RS has been predicted first by numerical analysis and has been validated experimentally, then, on the basis of the results of indentation tests performed at the micron scale on the metal layer. It is shown that this simple and fast methodology can return reliable results in the present context. Key words: Cu-CFC joints, residual stresses, indentation test, inverse analysis Acknowledgements: The present research work has been carried out within the framework of the European Network of Excellence on Knowledge-based Multicomponent Materials for Durable and Safe Performance (KMM-NoE) under the contract No. NMP-CT-00-. Financial support by EU is gratefully acknowledged. Running head title: Residual stresses in Cu-CFC components

3 Strain Page of 0 0. Introduction Residual stresses (RS) are the common consequence of production processes. They might be intentionally induced in metals (e.g., by shot penning) to confer resistance to fatigue and to some form of corrosion by inducing surface compression [], but in many cases they arise unintentionally due to thermal and/or mechanical processing such as bending, rolling, forging, casting and welding, with often negative consequences on the lifetime and reliability of structural components. In most situations, in fact, RS reduce the mechanical performance or cause the failure of manufactured products by increasing the rate of damage induced by fatigue, creep or environmental degradation, or by enhancing material brittleness, especially in non homogeneous material systems; see, e.g., [- ]. The present investigation concerns the presence of RS at the joint between a carbon fibre reinforced carbon composite (CFC) and copper (Cu) layer, to be used in the divertor of the International Thermonuclear Experimental Reactor (ITER). Details on this project can be found in []. CFC has excellent thermo-mechanical properties, such as high thermal conductivity, good thermal shock and thermal fatigue resistance. Due to these characteristics, CFC will be employed in ITER as plasma facing component coupled to a copper alloy (CuCrZr grade), which hosts the cooling channel of the heat sink. One of the most critical aspect of the design lifetime and reliability of this component manufacturing is the joint between CFC and the copper alloy, which must withstand high cyclic thermal, mechanical and neutron loads [-]. The main problem related to this joint is the large thermal expansion mismatch between the two materials, which can generate large RS at their interface. These stresses can be partially relaxed by the introduction of a ductile layer of pure copper between the CFC composite and the CuCrZr alloy as the yield limit of pure copper is much lower than that of the envisaged copper alloy, while their thermal expansion coefficients are very close. The RS thus induced in the intermediate pure copper layer have also to be carefully evaluated, then. To investigate them, specimens were manufactured as explained in Section, see e.g. Fig., and tested. Various techniques and diverse approaches, based on diffraction, impulse electric currents, hole drilling, slotting and layer removal (e.g. [,0]) are suitable to the purpose of evaluating RS, but their actual use is often limited by the reliability, complexity, cost and, to some extent, destructiveness of each measurement system.

4 Page of Strain 0 0 The method chosen for the present application, as a reasonable compromise between result accuracy and experimental efforts and costs, is based on the instrumented indentation test; see, e.g., [,] and references therein. A stressed specimen subjected to indentation is known to exhibit a different mechanical response in terms of indentation curve and imprint geometry if compared to an unstressed one. In particular, if the initial stress state is predominantly tensile, the material starts yielding at a smaller load applied to the indenter and therefore penetration depth is larger, when compared to the case of unstressed specimen, for the same load level. Vice versa if the stress state is compressive. This information can be exploited to provide an average value of the stress applied in the plane orthogonal to the indenter axis, if the stress directionality is unknown [-0]. When required, the principal stress directions may be recovered by the shape of the imprint geometry and by the amount of the material piling up left at the contact boundary between the sample and the indentation tool at its removal, which also turns out to be sensitive to the presence of initial stresses [-]. The relevant methodology is presented in Section. In the present application, some insight on the expected RS distribution in the joined samples has been preliminary gained by the simulation of the cooling process after Cu casting on the CFC substrate, see Section. This rather complex phenomenon involves temperature-dependent physical, metallurgical and mechanical properties which are seldom available, so reliable quantitative predictions of the RS are hardly returned. On the contrary, the spatial distribution of the RS is usually captured rather well, see e.g. []. The performed numerical analysis was then mainly intended to evaluate boundary effects, account taken of the small dimensions of the samples available for the experimental investigation. As a main result, it was shown that the extension of the zone were stresses are released due to the vicinity of the specimen free boundaries is rather restricted, but large enough to permit the identification, by indentation tests, of the constitutive parameters describing the actual response of the unstressed material sample at room temperature, see Section.. The preliminary thermo-mechanical analysis predicted also that the maximum RS are reached in a relatively wide area close to the joint, and that they are directed almost parallel to the interface between the Cu and CFC layers. This information has been exploited to identify the magnitude of the RS as shown in Section... Joined Sample Production The RS generated by the thermal expansion mismatch between the CFC composite and the CuCrZr alloy, which constitute the main ITER divertor components, can be partially relaxed by the

5 Strain Page of 0 0 introduction of a ductile layer of pure copper. Cu-CFC joint cannot be obtained by direct casting of copper on the CFC surface, due to the low wettability of molten copper on CFC. To improve this property, the surface of the composite has been modified by direct solid-state reaction at high temperature, depositing different metals inside the VI B group (including chromium, Cr) on the CFC surface. The next heat treatment led to the formation of a coherent and adherent thin carbide layer ( 0 µm) which is wetted by molten copper. The results of Cu-CFC joint development showed that the chromium modification was the best solution to have a good wettability and a strong interface; details can be found in [-]. The direct joining of Cu to CFC was performed in a special graphite sample holder, see Fig., where the modified CFC and the copper were placed and heated at 00 o C for 0 minutes, Ar flow. The power was then turned off and room temperature was reached under natural cooling condition. Specimens with dimensions... mm were cut to their final shape by a diamond saw and tested. Optical micrograph showed the expected continuous interfaces between Cr carbide and Cu and between Cr carbide and CFC [], see Fig.. In spite of the large thermal expansion mismatch between CFC and Cu, no cracks are revealed in the composites or at the interface after cooling from copper melting temperature to room temperature []. Copper layers of thickness up to mm have been successfully cast on CFC. As mentioned above, the intermediate ductile layer of pure copper between CFC and CuCrZr alloy is introduced to minimize RS arising from thermal expansion mismatch, nevertheless the problem is not solved completely because the thermal expansion coefficient of pure copper is similar to that of CuCrZr alloy. Therefore, some RS are expected in the Cu-CFC joint as well, although mitigated by the favorable mechanical properties of copper.. Preliminary Thermal Analysis Some insight on the RS distribution in the joined samples after their manufacturing can be gained by the simulation of the cooling process after copper casting on the CFC substrate. Despite the fact that reliable quantitative predictions are seldom returned, simplified thermal analyses can evaluate, with a reasonable degree of accuracy, the spatial distribution of the RS (see, e.g. []), which is mainly governed by the difference between elastic moduli and thermal expansion coefficient of the joined materials. Three dimensional finite element analyses have then been performed by a commercial code [] to simulate the slow cooling down from 00 C to room temperature (0 C), assuming that above 00 C high metal viscosity and annealing effects permit the stresses induced by the thermal

6 Page of Strain 0 0 expansion mismatch to quickly relax. In any case, most available temperature-dependent properties refer to the assumed temperature range only [-], as 0 C is the designed operating temperature for ITER components. Investigations on the material behavior up to a maximum C are then considered to be on the safety side. The selected constitutive model for copper was isotropic elastic-perfectly plastic, obeying Henky-Huber-vonMises (HHM) criterion. CFC was described instead as an orthotropic linear elastic solid. The assumed material parameters are taken from the available ITER literature [-] and are listed in Table. All properties, except the elastic modulus of Cu, were given average values over the considered temperature range, consistently with the significance and the accuracy of the available experimental information. In fact, CFC has almost constant elastic properties in the temperature range C, the only appreciable change being its elastic modulus along direction, which slightly varies between and 0 GPa []. Available data on CFC thermal expansion coefficient are rather scattered instead, depending on the information source. The reported values are however one order of magnitude lower than those relevant to copper, which shows a thermal expansion coefficient between. and. 0 - C - in the monitored temperature range 0-0 C, with rather small variation with respect to the assumed average value 0 - C -. Collected information about the inelastic behaviour of copper is also rather spread. This occurrence suggested to implement the simplest plasticity model in the present preliminary work. Different boundary conditions were introduced to account for the possible confining effect of the sample holder on the CFC during copper solidification. The principal results of these qualitative analyses were however mostly independent of the considered constraints, and can be summarized as follows, see Fig. : - the extension of the zone were stresses are released due to the vicinity of the specimen free boundaries is rather restricted; it is however large enough to permit the identification, by indentation tests, of the actual constitutive parameters describing the response of the unstressed material sample; - outside this relatively narrow released-stress zone, stresses assume rather uniform distributions along planes parallel to the Cu-CFC interface; - the removal of the stress component orthogonal to the external surface at the specimen boundaries does not affect much the distribution and the value of the most significant stress component, which is almost parallel to the interface; - in the copper layer, maximum tensile stresses are reached in a relatively wide area close to the interface, while compression is confined in a smaller region far from the joint.

7 Strain Page of 0 0. Identification of the Residual Stresses Different techniques can be exploited to measure RS in mechanical components. The methodology chosen for the present application is based on the instrumented indentation test supplemented by inverse analysis. This approach represents a reasonable compromise between result accuracy and experimental and computational efforts and costs. Indentation represents a practical methodology, nowadays extensively used for material characterisation in industrial environments, carried out by laboratory and in situ tests at different scale [,,-]. Local and overall material and surface properties such as elastic modulus, yield strength, scratch resistance, fracture energy can be inferred from the curves representing the imposed force versus penetration depth. Indentation curves also reflect the stress state in the material. In particular, if the stresses are predominantly tensile, penetration depths are larger than those exhibited by unstressed samples at the same load level; vice versa if the stress state is compressive [-]. Then, the copper layer of the considered joined material samples has been subjected to Vickers micro indentation, up to the maximum 0 mn load, in the locations schematically represented in Fig., at about mm,. mm and. mm from the interface. Relative shifts of the indentation curves relevant to different material point have been observed in the specimens under consideration. The average results of the tests performed in a row, at a fixed distance from the interface, are represented in Fig. together with their standard deviation. This picture confirms the main qualitative conclusions drawn from the results of the numerical thermo-mechanical analyses presented in Section. The observed scatter of the indentation curves relevant to each row is relatively small, while the curves relevant to different rows are clearly distinct. Notice that the penetration depth increases as the indented point becomes closer to the interface, singling out an increase of the RS intensity. In the present context, the fairly good agreement between the qualitative results of the indentation tests and of the numerical simulation suggest that the prevailing stress component is located close to the joint and is also parallel to the Cu-CFC interface. Therefore, the geometry of the residual imprints was not looked for, as otherwise proposed in [-]... Inverse Analysis Procedure Quantitative estimation of the maximum RS can be obtained by inverse analysis procedures that combine experiments and the simulation of the laboratory test as shown, e.g., in [-]. The

8 Page of Strain 0 0 inverse analysis problem can be formulated as the minimisation, with respect to the unknown parameters, of a norm which quantifies the overall discrepancy between the measured quantities and the corresponding values computed through a simulation model of the test [-]. In this approach, let h mi indicate the indentation depth corresponding to the force F mi in a number N of point selected from the experiment. Here subscript m means measured, and index i=,, N. Further, let hci ( z ) indicate the depth corresponding to F mi in the test simulation. Subscript c indicates a computed quantity, which is function of some assumed input parameters, like material properties or RS values, here collected by vector z. The discrepancy between measured and computed quantities can be defined by following euclidean norm: where N ( ) ( ) hci z hmi ω z = i= w () w hi represent weights on the displacement components h mi, assumed to be proportional to the variances which quantify hi the measurement noise. The optimum value of the sought parameters is represented by the entries of the vector z opt, which returns the minimum discrepancy. The minimisation of the objective function ω(z), defined by relation (), can be performed by a number of numerical methods implemented in widely available optimisation tools, e.g. []. For the present application, the so-called Trust Region algorithm has been satisfactorily employed. Details can be found in the reference manuals []. The indentation tests has been simulated by the finite element method, in the large deformation regime, exploiting the same commercial code used for the preliminary thermal analysis, like in other previous analyses of the indentation test; see, e.g., [-]. Since the maximum penetration depth is of the order of a few microns, see e.g. Fig., the material volume interested by indentation is rather small compared to the overall specimen dimension. A pure copper region has been then discretized as shown in Fig., account taken of the system symmetries. The Vickers diamond tip has been assumed perfectly rigid while HHM constitutive model has been chosen to interpret the material behaviour. As a main difference from the assumptions of the preliminary thermal analysis, either linear or exponential hardening has been also accounted for. The evolution of the elastic domain is then defined by the following yield limits: p p σy ( ε ) =σ y0+ Hε () or

9 Strain Page of 0 0 where the scalar value p σ ( ε ) =σ + () y y0 p n e ε p ε represents the total amount of the developed plastic deformation. The values of the mechanical parameters σ y0, H or n relevant to the copper layer have been evaluated first, according to the present procedure, starting from the experimental curves gathered indenting the stress-free specimen corners (e.g., location A in the sketch of Fig. a). Once these properties have been identified as shown in Section., the procedure has been applied again to evaluate the intensity of the RS, starting from the experimental indentation curve relevant to the test performed at location B. Details are given in Section.... Material Characterization The vicinity of the upper corners of the Cu layer to the specimen boundaries suggests that the indentation curves relevant to point A in the sketches of Fig. can be thought to be representative of the reference (stress free) material. This assumption is consistent with the qualitative picture of the stress distribution shown in Figs. and b, obtained by the preliminary thermal analysis. This occurrence has been further verified by considering the average indentation curves of a reference material sample, made of pure Cu and submitted to the same thermal treatment as the deposited layer, which was available in this case. These curves, drawn in Fig., match well with those obtained from the Cu-CFC specimen. The discrepancy function () defined for material characterization purposes depends on the actual mechanical properties of the copper layer, that is: the elastic Young modulus E and Poisson ratio ν, the yield stress σ yo and a parameter (either n or H) characterizing exponential or linear hardening, respectively. A preliminary assessment of the merits and of the limitations of the selected identification procedure has been carried out in []. The results of this investigation have shown that this methodology is rather robust and returns reliable values of the yield limit and the hardening modulus of ductile materials when experimental information is collected from the indentation curves only, while the identified Young modulus can be affected by much larger error. The elastic modulus at room temperature was then assumed to coincide with the value returned by the employed testing apparatus, which implements a popular formula proposed by Oliver and Pharr [,]:

10 Page of Strain 0 0 S E β( ν ) () A where S represents the initial slope of the unloading branch in the indentation curve and A indicates the contact area, while the semi-empirical calibration parameter β depends on the geometry of the indenter tip and on the equipment characteristics. Poisson ratio has been fixed to the value ν=0., taken from the literature and formerly used in the preliminary thermal analysis, due to the usually small sensitivity to this parameter of indentation results; see [,]. The estimated elastic modulus E was then found to be in good agreement with the reported literature data [,]; see Tables and. The initial yield stress σ y0 and the hardening parameter (either H or n, depending on the assumed plasticity model, see Section.) were then collected by vector z and numerically returned by the minimization of the discrepancy function (). Different initialization of the exploited Trust Region algorithm always returned almost identical results, listed in Table together with Young modulus E, thus confirming the robustness of the selected identification procedure. The correspondingly described material response to uniaxial load is represented in Fig.. From an engineering point of view, the two identified responses are rather similar schematization of the true material behavior. Fig. compares the experimental results relevant to the corner point A with the recalculated indentation curves obtained by the identified parameter set. Notice that both assumptions of linear and exponential hardening match the experimental data to the same extent. Therefore, there was no reason to prefer one or the other formulation... Stress Evaluation Indentation curves relevant to different points in the copper layer of the composite specimen reflect the corresponding RS as clearly shown, e.g., by Fig.. Fig. 0 compares the results of the tests performed at the reference (stress free) location A and at point B, close to the interface between the two different materials, where the maximum tensile RS is expected. Fig. 0 also shows that the slope of the unloading branch, which depends mainly on the elastic modulus E, is practically unaffected by the RS. The inverse analysis procedure outlined in Section. has been then applied once more. The exploited experimental data have been selected from the indentation curve relevant to the most critical specimen location (point B), while the sole unknown in the vector z that defines the

11 Strain Page 0 of 0 0 discrepancy function () is given now by the corresponding RS modulus. The material parameters used in the computations are those gathered from the previous identification step. The rather close RS values obtained from the two different assumed hypotheses on the material response are also listed in Table. The difference between the two estimations is of the order of 0%, which compares well with the various uncertainty sources in this calibration process. Both idealization match well the experimental results, as shown by the recalculated curves drawn in Fig... Closing Remarks A combined numerical experimental procedure has been employed to detect residual stresses (RS) in a mechanical component designed for fusion applications, made by casting a copper (Cu) layer on a carbon-fiber reinforced carbon composite (CFC). RS were induced in the component during its production process, mainly due to the mismatch between the thermal properties of the metal layer and of its support. A preliminary numerical simulation of the cooling process has been performed to single out the expected characteristics of the RS distribution. Literature data on the temperature dependent thermo-mechanical properties of Cu and CFC were employed for this analysis, which was intended to reliably return qualitative results only. The predicted spatial distribution of RS was then found to be in good agreement with the experimental outcome, as also shown, e.g., in []. The most significant RS values were then determined by inverse analysis of indentation data, after identification of the actual parameters governing the mechanical response of the cast copper in its stress-free condition, at room temperature. If compared with other available techniques for RS evaluation, indentation test has the advantages of being rather fast and to require easily available instrumentation. Further, the small volumes interested by indentation, permits to define the sought parameter field with high spatial resolution. The characteristic dimension of the sampled volume is in fact proportional to the penetration depth, which in turn varies with the square-root of the applied load. For the present application, the maximum penetration depth was of the order of a few microns, with a maximum applied load of 0 mn. If required, loads as low as µn could be considered as in [,], account taken of the local micro-structure (e.g., grain size) and of the representativeness of the selected material volume in the presence, e.g., of possible distributed defects or inclusions. The test could be performed close to the material separation interface where both RS and stress gradients are high, a significant piece of information not available from other measurement

12 Page of Strain 0 0 techniques []. Clearly, indentation is suitable for surface investigation only, unless combined with layer removal techniques. In the present application, the prevailing direction of the RS was known in advance, due to the continuity constraint at the interface between the two dissimilar materials and to the characteristics of the thermal source. In other situations, the commonly gathered information from the indentation test (namely, indentation force versus penetration depth) could be coupled with the mapping of the residual imprint to return the stress directionality as well, as shown e.g. in [,].. References. McClung, R.C. (00) A literature survey on the stability and significance of residual stresses during fatigue, Fatigue and Fracture of Engineering Materials and Structures, -0.. Deng, D., Murakawa, H., Liang, W. (00) Numerical and experimental investigations on welding residual stress in multi-pass butt-welded austenitic stainless steel pipe, Computational Materials Science,.. Schlosser, J., Martin, E., Henninger, C., Boscary, J., Camus, G., Escourbiac, F., Leguillon, D., Missirlian, M., Mitteau, R. (00) CFC/Cu bond damage in actively cooled plasma facing components, Physica Scripta T, Klaska, A.M., Beck, T., Wanner, A., Lohe, D. (00) Residual stress and damage development in the aluminium alloy EN AW- particle reinforced with AlO under thermal fatigue loading. Materials Science and Engineering A,.. Merola, M., Akiba, M., Barabash, V., Mazul, I. (00) Overview on fabrication and joining of plasma facing and high heat flux materials for ITER, Journal of Nuclear Materials -, -. Pintsuk, G., Compan, J., Linke, J., Majerus, P., Peacock, A., Pitzer, D., Rodig, M. (00) Mechanical and thermo-physical characterization of the carbon fibre composite NB, Physica Scripta T,.. Linke, J. (00) Plasma facing materials and components for future fusion devices development, characterization and performance under fusion specific loading conditions, Physica Scripta T,.. Noyan, I.C. and Cohen, J.B. () Residual Stresses, Elsevier, New York. 0. Lu, J. and James, M.R. () Handbook of Measurement of Residual Stresses, Fairmount Press, Lilburn, GA.

13 Strain Page of 0 0. Bhushan, B. () Handbook of Micro/nanoTribology, CRC Press, Boca Raton, FL.. Bolzon, G., Bocciarelli, M., Chiarullo, E.J. (00) Mechanical characterization of materials by micro-indentation and AFM scanning. Applied Scanning Probe Methods XII Characterization (B. Bhushan, H. Fuchs, Eds), Springer-Verlag, Heidelberg, -0.. Tsui, T.Y., Oliver, W.C., Pharr, G.M.() Influences of stress on the measurement of mechanical properties using nanoindentation: Part I. Experimental studies in an aluminum alloy, Journal of Materials Research, -.. Bolshakov, A., Oliver, W.C.; Pharr, G.M. () Influences of stress on the measurement of mechanical properties using nanoindentation: Part II. Finite element simulations, Journal of Materials Research, -.. Suresh, S., Giannakopoulos, A.E. () New method for estimating residual stresses by instrumented sharp indentation, Acta Materialia,. Taljat, B., Zacharia, T.; Kosel, F. () New analytical procedure to determine stress-strain curve from spherical indentation data, Int. J. Solids Structures, -.. Carlsson, S. Larsson, P.-L.(00) On the determination of residual stress and strain fields by sharp indentation testing. Part I: Theoretical and numerical analysis, Acta Materialia, -.. Carlsson, S. Larsson, P.-L.(00) On the determination of residual stress and strain fields by sharp indentation testing. Part II: Experimental investigation, Acta Materialia, -0.. Atar, E., Sarioglu, C., Demirler, U., Kayali, E.S., Cimenoglu, H. (00) Residual stress estimation of ceramic thin films by X-ray diffraction and indentation techniques, Scripta Materialia, Lepienski, C.M., Pharr, G.M., Park, Y.J., Watkins, T.R., Misra, A., Zhang, X. (00) Factors limiting the measurement of residual stresses in thin films by nanoindentation, Thin Solid Films -, -.. Zhao, M., Chen, X., Yan, J., Karlsson, A.M. (00) Determination of uniaxial residual stress and mechanical properties by instrumented indentation, Acta Materialia, -.. Lee, Y.-H., Kwon, D. (00) Measurement of residual-stress effect by nanoindentation on elastically strained (00) W, Scripta Materialia,.. Lee, Y.-H., Takashima, K., Kwon, D. (00) Micromechanical analysis on residual stressinduced nanoindentation depth shifts in DLC films, Scripta Materialia,.. Lee, Y.-H., Takashima, K., Higo, Y., Kwon, D. (00) Prediction of stress directionality from pile-up morphology around remnant indentation, Scripta Materialia,.

14 Page of Strain 0 0. Bocciarelli, M., Maier, G. (00) Indentation and imprint mapping method for identification of residual stresses, Computational Materials Science,.. Appendino, P., Casalegno, V., Ferraris, M., Grattarola, M., Merola, M., Salvo, M., (00) Direct joining of CFC to copper, Journal of Nuclear Materials -, -. Appendino, P., Ferraris, M., Casalegno, V., Salvo, M., Merola, M., Grattarola, M., (00) Proposal for a new technique to join CFC composites to copper, Journal of Nuclear Materials, 0-0. Casalegno, V., Salvo, M., Ferraris, M., Smeacetto, F., Merola, M., Bettuzzi, M. (00) Nondestructive characterization of carbon fiber composite/cu joints for nuclear fusion applications, Fusion Engineering and Design, 0-.. ABAQUS/Standard (00) Theory and User s Manuals, release.-, HKS Inc, Pawtucket, RI, USA.. Davis, J.W., Smith P.D. () ITER material properties handbook, Journal of Nuclear Materials -, -.. ITER Material Properties Handbook. ITER Document No. G MA W 0.. Piati, G., Boerman, D. () Hot Tensile Characteristics and Microstructure of a Cu-0. Cr- 0.0 Zr Alloy for Fusion Reactor Applications, Journal of Nuclear Materials, -. Bhattacharya, A. K. and Nix, W. D. () Finite element simulation of indentation experiments, International Journal of Solids and Structures, -. Jayaraman, S., Hahn, G. T., Oliver, W. C., Rubin, C. A. and Bastias, P. C. () Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests, International Journal of Solids and Structures, -. Dao, N., Chollacoop, N., van Vliet, K.J., Venkatesh, T.A. and Suresh, S. (00) Computational modeling of the forward and reverse problem in instrumented sharp indentation, Acta Materalia, -. Capehart, T.W. and Cheng,Y.-T. (00) Determining constitutive models from conical indentation: Sensitivity analysis, Journal of Materials Research, -. Bolzon, G., Maier, G. and Panico M. (00) Material model calibration by indentation, imprint mapping and inverse analysis, International Journal of Solids and Structures, -.. Bocciarelli, M., Bolzon, G. and Maier, G. (00) Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping, Mechanics of Materials, -.. Jang, J.-I., Choi, Y., Lee, J.-S., Lee, Y.-H., Kwon, D., Gao, M., Kania, R. (00) Application of instrumented indentation technique for enhanced fitness-for-service assessment of pipeline crack, International Journal of Fracture, -.

15 Strain Page of 0 0. Bui, H.D. (). Inverse Problems in the Mechanics of Materials: an Introduction, CRC Press, Boca Raton, FL.. Stavroulakis, G., Bolzon, G., Waszczyszyn, Z. and Ziemianski, L. (00) Inverse Analysis. Comprehensive Structural Integrity (B. Karihaloo, R.O. Ritchie and I. Milne eds.) Elsevier Science Ltd, Kidlington (Oxfordshire), UK, Vol., Chapter.. Mroz, Z. and Stavroulakis, G., eds. (00) Parameter Identification of Materials and Structures, Springer-Verlag, Berlin.. Matlab (00) User s guide and optimization toolbox, release., The Math Works Inc, USA.. Oliver, W.C., Pharr, G.M. () An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, Journal of Materials Research, -.. Oliver, W.C., Pharr, G.M. (00) Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology, Journal of Materials Research, -0.. Fiori, F., Calbucci, V., Casalegno, V., Ferraris, M., Salvo, M., Giuliani, A., Manescu, A. and Rustichelli, F. (00) Neutron diffraction measurement of residual stresses in CFC/Cu/CuCrZr joints for nuclear fusion technology, Journal of Physics: Condensed Matter 0, 00 (pp).

16 Page of Strain 0 0 Cu CFC Elastic modulus [GPa] at 0 C at 00 C direction 0 direction direction Lateral contraction ratio Yield limit [MPa] Thermal expansion [0 - C ¹] direction 0. direction 0. direction - direction 0. direction. direction Table : Assumed material properties for the preliminary thermal analysis []. All properties, except the elastic modulus for copper, are given average values over the considered temperature interval 0 C to 00 C. CFC directions (,,) are indicated in Fig..

17 Strain Page of 0 0 Exponential hardening Linear hardening E [GPa] E [GPa] σ y0 [MPa] 0 σ y0 [MPa] n 0.0 H [MPa] 0 σ r [MPa] 0 σ r [MPa] Table : Calibrated material properties of the Cu layer (elastic modulus E; initial yield stress σ y0, hardening parameter n or H, according to the hypothesis of either linear or exponential hardening) and the correspondingly estimated maximum residual stress σ r.

18 Page of Strain 0 0 Fig. : Cu-CFC material specimen production. Cu CFC

19 Strain Page of 0 0 Fig. : Optical micrograph of the Cu-CFC interface.

20 Page of Strain 0 0 (a) (b) (c) Fig. : Preliminary estimation of the RS distribution in the material sample after cooling process. The front face in the finite element representation corresponds to the middle specimen surface. Pictures (a) and (b) visualise the similar distribution of the expected stress components parallel to the interface between the two dissimilar materials, along spatial directions and, respectively; picture (c) refers to the much smaller stresses acting along direction, normal to the joint.

21 Strain Page 0 of 0 0 (a) (b) Fig. : Schematic representations of the location of the performed indentation tests (a) and graphical superposition of the indentation locations to the map of the expected RS distribution, according to the output of the performed preliminary thermal analysis (b). The colour picture in (b) refers to the distribution of stresses parallel to the joint, already visualised in Fig. (a). B A

22 Page of Strain 0 0 Load [mn] mm distance. mm distance. mm distance 0 Penetration depth [µm] Fig. : Average results and standard deviation of indentation tests performed at a fixed distance from the interface, as specified in the legend. The sampled points are schematically represented in Fig..

23 Strain Page of 0 0 Fig. : The finite element mesh used in the simulation of the performed indentation tests.

24 Page of Strain 0 0 Load [mn] Reference Cu sample (average) Cu-CFC imprint A 0 Penetration depth [µm] Fig. : Comparison between the indentation curves relevant to test performed at the reference location A in the copper layer of the Cu-CFC specimen (see the sketch in Fig. a) and in a pure copper specimen.

25 Strain Page of 0 0 Stress [MPa] Exponential hardening Linear hardening 0 0 Strain [%] Fig. : The identified uniaxial material behaviour, corresponding to the mechanical parameters listed in Table.

26 Page of Strain 0 0 Load [mn] Exponential hardening Experimental Linear hardening 0 Penetration depth [µm] Fig. : Comparison between the experimental indentation curves and the corresponding ones recalculated with the identified material parameters listed in Table, for the reference (stress free) material.

27 Strain Page of 0 0 Load [mn] Cu-CFC imprint A Cu-CFC imprint B 0 Penetration depth [µm] Fig. 0: Comparison between the indentation curves relevant to the test performed at the reference (stress free) location A and at point B in the copper layer of the Cu-CFC specimen; see the sketch in Fig. a.

28 Page of Strain 0 0 Load [mn] Exponential hardening Experimental Linear hardening 0 Penetration depth [µm] Fig. : Comparison between the experimental indentation curves and the corresponding ones recalculated with the identified material parameter set, for the stressed material point B, indicated in the sketch of Figure a.