Slow crack growth in polycarbonate films

Introduction. -Solids with a single crack usually break at a critical rupture stress. However, experiments [1] show that a given solid submitted to a subcritical stress breaks after a certain amount of time. Therefore, understanding the mechanisms of subcritical macroscopic fracture growth in solids has become an important goal of fracture physics in order to improve the resistance of structures to failure. Recent experimental works [2,3] have shown that subcritical crack growth in paper can be successfully described by a thermal activation model for elastic brittle media. In this letter, we present an experimental study of slow growth of a single crack in a polycarbonate film which is a highly non-brittle material. We observe that a large flame shaped area, the process zone, forms ahead of each crack tip. We find that the dependence of the process zone length with the applied stress, during the crack growth, is in reasonable quantitative agreement with the Dugdale-Barenblatt model. In that respect, polycarbonate appears to be a good model material to understand the mechanisms of crack growth in non-elastic media. We show that the crack growth curve obeys remarkable scaling properties that are not theoretically understood yet.

The experimental setup and the experiment. -The experiment consists in loading 125µm thick isotropic polycarbonate films (height 21cm, length 24cm) with uniaxial and constant imposed stress σ. The polycarbonate films used are made of Bayer Makrofol R and present the properties of bulk material. An initial crack of length ℓ i is initiated at the center of each polycarbonate sample using calibrated blades of different lengths (from 0.5cm to 3cm). Then, a constant force F c is applied to the film perpendicularly to the crack direction, so that we get a mode 1 crack opening type. For more details about the setup see [2,3]. A high resolution and high speed camera (Photron Ultima 1024) is used to follow the crack growth.

We follow the growth of the single linear fracture and its process zones, under constant applied stress σ, till the total rupture of the sample. The applied stress σ is chosen such that crack growth is slow, i.e., smaller than the critical one, σ c , above which a fast crack propagation occurs.

Mechanical properties of polycarbonate films. -In order to characterize the material in which the crack will grow, we performed some preliminary experiments on polycarbonate films, without crack, submitted to uniaxial deformation at a constant deformation rate (46.25µm.s -1 ). A typical experimental stress-strain plot is presented in figure 1. The polymer films show the classical behavior of a plastic material with a quasi-elastic behavior for small strains followed by a bell profile and a plateau. The different characteristic values observed on this graph are in good agreement with the ones measured by Lu and Ravi-Chandar in bulk polycarbonate [4]. We measured the experimental values of the maximum reachable stress, σ p = 5.2 10 7 N.m -2 , the plastic plateau stress σ plat = 4.45 10 7 N.m -2 and the Young modulus for small strains Y = 194 10 7 N.m -2 .

The flame shaped process zone ahead of the crack tip. -In each experiment, during the loading phase of the film, a macroscopic flame shaped process zone appears at each tip of the crack and grows with the applied stress (cf. figures 2 and 3). This zone was previously noticed by Donald and Kramer [5]. In the late loading stage, the fracture may also grow a little. Consequently, the real experimental initial condition, obtained when the constant stress σ is reached, is not exactly ℓ i . During the imposed stress stage, the process zone and the fracture are both growing till the final breakdown of the sample in a way that the fracture never catches up the process zone tip.

Inside the process zone, the film is subjected to a thinning which brings its thickness from 125µm to about 70µm (measured on post-mortem samples). It is worth noticing that on microscopic images (cf. figure 3) one can see in the process zone the presence of striations quasi-parallel to the fracture front with a wave length of about 22µm. These striations seem to be thickness oscillations of the film. It is still an open question whether this process zone,

PSfrag replacements ℓ crack ℓpz Fig. 2 -Image of a crack in a polycarbonate film with its macroscopic process zone at each tip; ℓ crack is the crack length and ℓpz is the process zone length from tip to tip.

once it has been formed, continues to behave as a visco-plastic zone or as an elastic zone with an effective macroscopic Young modulus different from the one of the rest of the film. Understanding the mechanical nature of the process zone is the key to reach a model of fracture growth in polycarbonate.

Dependence of the process zone length on the fracture length. -The experimental relation between the process zone length (defined on figure 2), ℓ pz , and the crack length, ℓ crack , during the crack growth

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