Fatigue analysis of brittle materials using indentation flaws

Abstract

A two-part study has been made of the fatigue characteristics of brittle solids using controlled indentation flaws. In this part a general theory is developed, with explicit consideration being given to the role played by residual contact stresses in the fracture mechanics to failure. The distinctive feature of the formulation is a stress intensity factor for well-defined indentation cracks, suitably modified to incorporate the residual component. Taken in conjunction with a standard power-law crack velocity function, this leads to a differential equation for the dynamic fatigue response of a given material/ environment system. Reduced variables are then introduced to facilitate generation of "universal" fatigue curves, determined uniquely by the crack velocity e'xponent, n. A scheme for using these curves to evaluate basic fracture parameters from strength data is outlined. In this way the foundation is laid for lifetime predictions of prospective brittle components, as well as for reconstruction of the crack velocity function. One of the major advantages of the analysis is the manner in which the residual stress parameters are accommodated in the normalized fracture mechanics equations: whereas it is understood that all strength data are to be taken from test pieces in their as-indented state, so making it unnecessary to have to resort to inconvenient stress-removal procedures between the contact and failure stages of testing, a priori knowledge of the residual stress level is not required. The method is proposed as an economical route to materials evaluation and offers physical insight into the behaviour of natural flaws.

Controlled Indentation Flaws for the Construction of Toughness and Fatigue Master Maps

“…Thus, eq (9a) may be inverted to obtain n directly from n I, and eq (9b) similarly (in conjunction with measured values of 0" m and cm) to obtain Vo from A'. It is again seen that initial crack size does not enter the results, as long as the condition co<c m remains operative [9].…”

“…In the event of any pre-existent stress acting on the crack a third term would have to be included in eq (1) [4,9]. Other than to note that this potential complication needs to be heeded when preparing the surfaces of test specimens we shall consider it no further in our mathematical derivations.…”

“…A controlled-flaw technique which effectively eliminates the statistical component from strength testing has been described in a series of recent articles [3][4][5][6][7][8][9][10][11][12]. A single dominant flaw of predetermined size and geometry is introduced into the prospective tensile surface of each specimen using a standard diamond indenter.…”

“…It is then not possible to investigate these two elements of the 453 problem in any truly independent way. Evaluation of material parameters becomes a mere exercise in statistical data manipulation, with little or no physical insight into the nature of the critical flaws responsible for failure [1-2V This probabilistic approach makes it difficult to assess the relative merits of different materials from the standpoint of intrinsic properties alone.A controlled-flaw technique which effectively eliminates the statistical component from strength testing has been described in a series of recent articles [3][4][5][6][7][8][9][10][11][12]. A single dominant flaw of predetermined size and geometry is introduced into the prospective tensile surface of each specimen using a standard diamond indenter.…”

Indentation Fractography: A Measure of Brittleness

“…For example, by inverting eq (11) one can evaluate Kc in terms of strength and indentation load (given, of course, an appropriate "calibration" of the coefficient in this equation), without any recourse to the measurement of crack dimensions [59]. Similarly, one can combine the K relation in eq (8) with an appropriate crack velocity function to obtain material-environment fatigue parameters (e.g., exponent n in power-law velocity function) [53,[60][61][62]. In all these analyses a proper quantitative evaluation requires a full accounting of the residual stress term.…”