We investigate experimentally and theoretically the dynamics of a crack front during the microinstabilities taking place in heterogeneous materials between two successive equilibrium positions. We focus specifically on the spatio-temporal evolution of the front, as it relaxes to a straight configuration, after depinning from a single obstacle of controlled strength and size. We show that this depinning dynamics is not controlled by inertia, but instead, by the rate dependency of the dissipative mechanisms taking place within the fracture process zone. This implies that the crack speed fluctuations around its average value vm can be predicted from an overdamped equation of motion (v −vm)/v0 = (G−Gc(vm))/Gc(vm) involving the characteristic material speed v0 = Gc(vm)/G c (vm) that emerges from the variation of fracture energy with crack speed. Our findings pave the way to a quantitative description of the critical depinning dynamics of cracks in disordered solids and open up new perspectives for the prediction of the effective failure properties of heterogeneous materials.Woods, nacre, bones or rationally designed artificial materials, are all heterogeneous solids, with mechanical properties far exceeding those of their constitutive components. Understanding the role of microscale heterogeneities on the macroscale fracture behavior of solids still remains a query. This becomes especially relevant now, as rapid developments in microfabrication techniques allow the tailoring of microstructures at ever smaller scales, yielding new types of composites, known as meta-materials, with unprecedented mechanical properties [1][2][3][4][5][6]. Recently, significant progresses were made for weakly heterogeneous brittle solids where models describing a crack front as a deformed interface pinned by tough obstacles have been successfully applied [7][8][9][10][11]. The homogenized fracture properties can be computed exactly within the so-called weak pinning limit [12], where the elastic energy release rate G balances the fracture energy G c at any time and any position along the front. This approach holds for weak variations of toughness along the propagation direction. The crack evolution is then smooth and can be properly approximated by a continuous succession of equilibrium front configurations [13,14]. This approach was successfully used to design weakly heterogeneous systems with improved and new macroscopic failure properties [15][16][17][18].However, most natural and engineered materials have a microstructure composed of discontinuous heterogeneities which cannot be described within the weak pinning regime. The strong pinning regime that predominates for large toughness gradients challenges standard homogenization approaches. Crack propagation is not quasi-static but proceeds by intermittent and local micro-instabilities. Further, for a disordered distribution of obstacles, crack growth takes place close to the socalled depinning critical transition [19][20][21], so that the h s d = 141 �m, C = 1.2, v m = 24 �m/s FIG. 1. (a...

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