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This paper extends the M -integral concept (Eshelby in The continuum theory of lattice defects, solid state physics, Academic Press, New York, 1956; The energy momentum tensor in continuum mechanics, inelastic behavior of solids, McGraw-Hill, New York; and J Elast 5:321–335, 1975; Knowles and Sternberg in Arch Rat Mech Anal 44:187–211, 1972; Budiansky and Rice in ASME J Appl Mech 40:201–203, 1973; Freund in Int J Solids Struct 14:241–250, 1978; Herrmann and Herrmann in ASME J Appl Mech 48:525–530, 1981; King and Herrmann in ASME J Appl Mech 48:83–87, 1981) to study the degradation of a brittle plane strip caused by irreversible evolution: the coalescence between two holes under monotonically increasing loading. Attention is focused on the change of the M -integral before and after coalescence of two neighborly located holes. Different orientations of the two holes and different coalescence path curves connecting the rims of the two holes are studied in detail. Finite element analyses reveal that different orientations of the two holes lead to different critical values of the M -integral, at which the maximum hoop stress (i.e., the stress along the rim of a hole) reaches the material strength and coalescence occurs, and that the minimum critical value of the M -integral approximately corresponds to the minimum critical tensile loading as the orientation varies. It is concluded that the M -integral as a configurational force does play an important role in description of the damage extent and damage evolution. However, it only provides some outside variable features . This means that the complete failure mechanism due to damage evolution cannot be governed by a single parameter M C as proposed by Chang and Peng [ASCE J Eng Mech 130(5):589–598, 2004]. It is found that there is an inherent relation between the M -integral and the reduction of the effective elastic moduli as the orientation varies. The larger the M -integral is, the larger the reduction is. Of great significance is that the M -integral is inherently related to the change of the total potential energy (CTPE) for a damaged brittle material regardless of the detailed damage features or damage evolution. Therefore, this provides a convenient and useful experimental technique to measure the values of the M -integral for a damaged brittle material from initial damage to final failure without use of many strain gages (King and Herrmann in ASME J Appl Mech 48:83–87, 1981).
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