Representative and statistical volume elements for grain boundary networks: A stereological approach

Critchfield, Tyler; Johnson, Oliver K.

doi:10.1016/j.actamat.2019.12.029

Cited by 8 publications

(1 citation statement)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Salahouelhadj and Haddadi [16] estimated RVE sizes for copper polycrystals using homogenisation techniques and finite element simulations. Among many other such studies, of special relevance to the present effort is the recent stereological approach of Critchfield and Johnson [17] where they select multiple random samples from within a numerically simulated domain in order to statistically estimate the RVE size. On the experimental side, a few studies have developed methods of measuring RVE size, with one of the earliest being by Liu [18] who introduced the idea of using full-field strain measurements to determine the size of a strain-based RVE.…”

Section: Introductionmentioning

confidence: 99%

Measuring representative volume elements from high‐resolution grain‐scale strain fields

Vieira

Lambros

2022

Strain

View full text Add to dashboard Cite

Most crystalline materials present a highly heterogeneous response at the microscale, which can be affected by both internal factors (such as microstructural parameters) and external factors (such as loading). Relating microscale inhomogeneities to the macroscale response of a material requires the use of homogenisation techniques, usually based on the concept of a representative volume element (RVE)-the smallest volume of material that represents the global average response. In this work, we present a new and robust experimental method of measuring the size of a strain-based RVE from high-resolution grain-scale strain fields obtained using digital image correlation (DIC). The proposed method is based on the statistical (stereological) nature of the RVE, which has been widely adopted in numerical studies, and involves dividing a strain field into randomly selected regions of varying sizes and statistically analysing the distributions of average strains within them. To validate the new method, we generate a large number of synthetic strain fields from a fractional Gaussian noise algorithm. The proposed stereological method is shown to be capable of producing reliable RVE measurements from a very large range of possible microscale strain fields while at the same time being robust in that it can produce RVE measurement results even in cases where other existing methods may be unable to do so. The proposed method has a low field-of-view requirement, only needing a field-of-view about 1.2 times as large as the RVE to produce reliable measurements. In addition, the stereological method offers significant flexibility since its statistical nature allows for control over how strict the RVE measurement should be in each case.

show abstract

Section: Introductionmentioning

confidence: 99%