Issue 30

D. Nappini et alii, Frattura ed Integrità Strutturale, 30 (2014) 394-402; DOI: 10.3221/IGF-ESIS.30.47 396 D IRECT ANALYSIS Parameters evaluated from load-indentation depth curves nstrumented indentation is widely used to probe the elastic and plastic properties of engineering materials. The indentation test can only provide the characteristic load P vs. penetration depth δ curve, a sequence of measured values ( exp exp i i P ,δ ), and a reverse analysis is therefore required to estimate the mechanical properties of materials (Fig. 1). Figure 1 : (a) Scheme of spherical indentation on a homogeneous, isotropic semi-infinite bulk specimen; (b) typical indentation load– depth curves obtained from an experiment; (c) the uniaxial stress–strain (σ–ε) curve of a power-law hardening solid. Elastic modulus, E, has been widely employed to obtain damage evolution, using the fact that it shows a progressive degradation with damage. Therefore, by measuring the value of E it is possible to indirectly measure the value of damage according to the following common equation: 0 DM 1 E E   where E is the effective modulus of damaged material and E 0 is the modulus of virgin material. The stress–strain (σ-ε) curves of the materials are represented in Hollomon like power law form, identified by three parameters: the Young modulus, the stress of proportionality limit, σ 0 , and the strain-hardening exponent, n. The σ-ε curve can be deduced from indentation test by means an optimization algorithm that minimize the function exp exp 0 i i χ(E, n, σ , P ,δ ) , which represents the global distance between the measured points and the theoretical curve defined by the material properties E, σ 0 , n [18-20]. The reverse analysis of the indentation test involves three-axial stress state, as well as the highly nonlinearity of material behaviour, and the complexity of contact problem due to the presence of friction and size effect. Therefore it is the critical step of the whole procedure. By evaluating E by means of indentation tests it is possible to estimate the damage. The promising potential of the idea is related to the possibility to correlate the damage parameter to stress and temperature fields, but the measurement of the elastic modulus obtained from σ-ε curves were not considered in this work enough accurate in consequence of a substantial data dispersion. In order to set up the effective capability of the instrumented spherical indentation testing system to evaluate variations in the material properties due to damage resulting from long time service, the collected load-indentation depth curves were systematically analysed. In particular the parameters below listed were evaluated (Fig. 2): - The maximum displacement, δ max . - The final depth, δ f , i.e. the permanent depth of penetration after the indenter is fully unloaded. - The elastic unloading contact stiffness, S (dP/dδ), defined as the slope of the portion of the curve during the initial stages of unloading. - The value δ i of the intercept on x-axes of the line with slope S starting from the maximum of the curve. - The area included by loading and unloading curve corresponding to the total work done by the indenter, W. - The value of diameter at the rim of the impression, d, evaluated in function of the value of penetration depth δ acquired by the LVDT transducers: I a) b) c)