Predicting peak stresses in microstructured materials using convolutional encoder–decoder learning

This work presents a machine-learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective response and overall structure of stress fields. However, their ability to predict peak – which are of critical importance to failure – is unexplored, because the peak-stress clusters occupy a small spatial volume relative to the entire domain, and hence require computationally expensive training. This work develops a deep-learning-based convolutional encoder–decoder method that focuses on predicting peak-stress clusters, specifically on the size and other characteristics of the clusters in the framework of heterogeneous linear elasticity. This method is based on convolutional filters that model local spatial relations between microstructures and stress fields using spatially weighted averaging operations. The model is first trained against linear elastic calculations of stress under applied macroscopic strain in synthetically generated microstructures, which serves as the ground truth. The trained model is then applied to predict the stress field given a (synthetically generated) microstructure and then to detect peak-stress clusters within the predicted stress field. The accuracy of the peak-stress predictions is analyzed using the cosine similarity metric and by comparing the geometric characteristics of the peak-stress clusters against the ground-truth calculations. It is observed that the model is able to learn and predict the geometric details of the peak-stress clusters and, in particular, performed better for higher (normalized) values of the peak stress as compared to lower values of the peak stress. These comparisons showed that the proposed method is well-suited to predict the characteristics of peak-stress clusters.

Flaw Detection in Highly Scattering Materials Using a Simple Ultrasonic Sensor Employing Adaptive Template Matching

Ultrasonic sensors have been extensively used in the nondestructive testing of materials for flaw detection. For polycrystalline materials, however, due to the scattering nature of the material, which results in strong grain noise and attenuation of the ultrasonic signal, accurate detection of flaws is particularly difficult. In this paper, a novel flaw-detection method using a simple ultrasonic sensor is proposed by exploiting time-frequency features of an ultrasonic signal. Since grain scattering mostly happens in the Rayleigh scattering region, it is possible to separate grain-scattered noise from flaw echoes in the frequency domain employing their spectral difference. We start with the spectral modeling of grain noise and flaw echo, and how the two spectra evolve with time is established. Then, a time-adaptive spectrum model for flaw echo is proposed, which serves as a template for the flaw-detection procedure. Next, a specially designed similarity measure is proposed, based on which the similarity between the template spectrum and the spectrum of the signal at each time point is evaluated sequentially, producing a series of matching coefficients termed moving window spectrum similarity (MWSS). The time-delay information of flaws is directly indicated by the peaks of MWSSs. Finally, the performance of the proposed method is validated by both simulated and experimental signals, showing satisfactory accuracy and efficiency.

Extreme Clusters of Grains in Random Microstructures of Polycrystals

It was experimentally observed that in polycrystalline materials under low macro loading of the specimen the first sites of failure initiation take place in the specific clusters of few grains. In some grains of these extreme clusters, the local (meso-) strains and stresses are high enough to cause first damages or plastic slips. In the stochastic microstructure of polycrystals, the formation of an extreme cluster is random and rare. Nevertheless, they govern the failure process initiation and can severely affect the reliability of polycrystalline machine parts. It is time and resource consuming to search and investigate extreme clusters on the real specimens of polycrystalline materials experimentally. A theoretical tool is desirable. Here we present the powerful computational method to look for extreme clusters, to investigate their possible patterns, and to evaluate the absolute maximums of local strains/stresses that can be achieved in these clusters. The experimentally observed clusters consist of few (3-4) preferably oriented neighboring grains or even of one big supergrain. The strain and stress bursts arise due to an interaction of the grains. One can expect that in bigger clusters, larger local bursts of fields can be generated. We found the typical forms of the extreme clusters (small and big) in four different polycrystals with grains of a weak and strong anisotropy for the case of uniaxial tension. In all regarded cases, the extreme clusters have the forms of the symmetrical patterns. In big clusters of highly anisotropic grains, the maximum of mesostrain exceeds the macrostrain by several times. In clusters of weakly anisotropic grains, the local strain concentration is rather moderate (tens of percents).

Efficient Fitting of 3D Tessellations to Curved Polycrystalline Grain Boundaries

The curvature of grain boundaries in polycrystalline materials is an important characteristic, since it plays a key role in phenomena like grain growth. However, most traditional tessellation models that are used for modeling the microstructure morphology of these materials, e.g., Voronoi or Laguerre tessellations, have flat faces and thus fail to incorporate the curvature of the latter. For this reason, we consider generalizations of Laguerre tessellations—variations of so-called generalized balanced power diagrams (GBPDs)—that exhibit non-convex cells. With as many as ten parameters for each cell, it is computationally demanding to fit GBPDs to three-dimensional image data containing hundreds of grains. We therefore propose a modification of the traditional definition of GBDPs that allows gradient-based optimization methods to be employed. The resulting reduction in runtime makes it feasible to find approximations to real experimental datasets. We demonstrate this on a three-dimensional x-ray diffraction (3DXRD) mapping of an AlCu alloy, but we also evaluate the modeling errors for simulated data. Furthermore, we investigate the effect of noisy image data and whether the smoothing of image data prior to the fitting step is advantageous.