Termal fluctuations effect on crack propagation and decohesion phenomena

Fracture propagation and decohesion phenomena are widely present in various physical, biological, and technologicalsystems. The study of these phenomena has applications that extend from classical mechanical sciences (e.g., crack propagationin solids) to emerging fields such as advanced materials, nanotechnology [1, 2], and soft materials [3], includingrubber-like and biomaterials (e.g., cell adhesion and de-adhesion, DNA denaturation) [4, 5]. In many of these fields, thermaleffects may play a crucial role. For instance, the required force for DNA denaturation or for the peeling of a thin filmfrom a substrate typically diminishes as temperature rises. This reduction is often attributed to thermal fluctuations, whichfacilitate the exploration of phase space [6]. In some cases, such effects can lead, as temperature grows, to a spontaneousevolution of fracture and decohesion fronts. Despite extensive experimental studies and numerical simulations exploringthe relationship between thermal fluctuations and mechanical properties, a comprehensive theoretical approach that fullyintegrates temperature effects remains elusive.Here, based on previous studies by the authors [12, 13], we address this gap, with the main goal of rigorously elucidatingthe influence of temperature on decohesion and material failure. One of the challenges in this analysis is to bridge thenano-scale with the meso-scale through a multiscale approach. In the presented work, this paradigm is employed by concurrentlyintroducing a discrete and a continuum model of the mode I fracture. As demonstrated in [12, 13], this approachensures that both the local and global minimizers of the discrete model converge to the equilibria of the mesoscopic modelin the continuum limit, thereby preserving all the essential physical information of the discrete (low-scale) lattice. Thediscrete model lets us incorporate temperature effects through the tools of classical equilibrium statistical mechanics [8, 9],measuring fluctuations at molecular- or nano-scales, whereas the continuous model enables the description of elasticityand energy release rate at the mesoscale.Figure 1 shows the general idea we used to study crack propagation, adhesion, and decohesion using a multiscaleapproach. Starting from the macroscopic description of an elastic body containing a crack subjected to tensile stress,we first consider a discrete model composed of repetitions of identical units at a small scale (Figure 1 a). Applyingdownscaling (Figure 1 b) and c), we first consider a discrete prototypical model composed of perfectly elastic elements(representing the two elastic half planes) connected by elasto-fragile elements (Figure 1 d). We then study the continuumlimit (i.e. the limiting value of the total energy when the number of units of the discrete system tends to infinity) to gaininsight into mesoscopic phenomena. The deduction of continuous, compact formulations is highly desirable both forthe deduction of multiscale approaches and for clearer physical interpretability of the analytical results. Through thisapproach, building on the Griffith energy criterion [7], we are then able to extend the established criterion for fracture anddecohesion to incorporate the influence of thermal fluctuations. The main innovation of our approach involves substitutingtotal mechanical energy with thermodynamic quantities, specifically free energies.The considered prototypical model, extensible in many possible materials and geometric directions at the expensesof physical clarity and analyticality, allows us both to effectively capture all main qualitative features of the fracturephenomenology and to integrate temperature effects. Moreover, all results are deduced in closed analytical form, allowingfor deeper description of the fundamental underlying physical phenomena. In addition, these simple models allow us todescribe either the case where fracture or decohesion propagates from one end, or the configuration where the broken partis inside the system, including scenarios with multiple bubbles in the system (e.g., multiple bubbles in DNA). In the lattercase, we can determine solutions where these bubbles coalesce before failure.Interestingly, our approach unveils a classical critical behavior, with the critical load decreasing according to thelaw sqrt(1 − T/Tc) as the temperature increases [10, 11]. As a consequence of the temperature effects, we prove that incorrespondence to the critical temperature Tc , the system undergoes a phase transition, corresponding to the completerupture without the application of any mechanical load.In analogy with the quasicontinuum framework [14], the proposed description of thermal effects can be incorporatedinto real physical systems by interpreting the model as a representation of the process zone in decohesion and crackpropagation phenomena. This is the objective of our future investigations.