Determination of the Gurson–Tvergaard damage model parameters for simulating small punch tests

Abstract

A B S T R A C TThe objective of the final small punch test (SPT) is to determine the fracture properties of materials, such as fracture toughness, when not enough material is available for the conduct of conventional fracture tests. The damage model developed by Gurson, and subsequently modified by Tvergaard and Needleman (GTN), allows for the numerical simulation of the elastic-plastic behaviour until fracture. This model is based on several constitutive material parameters that must be calibrated if the model is to be properly applied. In this paper, we develop a consistent methodology for the identification of the GTN damage parameters based on the adjustment of the load-displacement curve obtained in the SPTs. The methodology presented is applicable to simulating other different SPTs with different thicknesses and test temperatures. Also, the three-dimensional modelling developed will be useful in the future for analysing the possible anisotropy exhibited by some materials. The next step in the simulation will be to determine its validity in other stress fields with different triaxiality ratios, like the one present in CT specimens, the ultimate goal being to allow for the estimation of the material fracture toughness.Keywords damage modelling; Gurson-Tvergaard model; small punch. 0 , b 1 , b 2 , b 11 , b 22 , b 12 = quadratic model constants d = punch diameter (mm) D = diameter of the tensile test specimen (mm) e = specimen thickness (mm) E = Young's modulus (MPa) f = porosity or void volume fraction f * = modified porosity f 0 = initial void volume fraction f c = critical void volume fraction f F = void volume fraction at failure f N = void nucleation volume fraction f * u = constant failure void volume fractioṅ f = void volume fraction incremenṫ f growth = growth void volume fraction incremenṫ f nucleation = nucleation void volume fraction increment g 1 (ε n , f N ) = quadratic model K = strength coefficient m = slope Correspondence: I. I. Cuesta. N O M E N C L A T U R E b

Correlation between small punch and CVN impact tests for evaluation of cryogenic fracture characteristics of isothermally-aged nitrogen-containing austenitic stainless steels

“…There are several relationships between the parameters of CVN impact test and those of SP test 7,8,12 ; nevertheless, there is no report about a linear relation between the energy of both testing methods. The relationship between E CVN and E SP seems to be related to the presence of aging-induced embrittlement because the intergranular precipitation during the aging process caused the decrease in energy for these steels.…”

Damage modeling in Small Punch Test specimens

“…It therefore comes as no surprise that efforts to characterize the initiation and subsequent propagation of cracks in SPT specimens have mostly employed models that account for the nucleation, growth and coalescence of microvoids (see, e.g., [8,9,11,12,18] and references therein). The model by Gurson [19], later extended by Tvergaard and Needleman [20], is by far the most frequent choice, but other models -such as the one by Rousselier [21] -have also been employed [9].…”

“…The aforementioned testing methodology, commonly known as Small Punch Test (SPT), employs very small specimens (generally, 8 mm diameter and 0.5 mm thickness) and may be considered as a non-destructive experiment. The SPT has consistently proven to be a reliable tool for estimating the mechanical [2,3] and creep [4,5] properties of metallic materials and its promising capabilities in fracture and damage characterization have attracted great interest in recent years (see, e.g., [6][7][8][9][10][11][12][14][15][16][17][18]). …”

“…These models are able to quantitatively capture the experimental results by fitting several parameters that account for the ductile damage mechanisms taking place. A variety of inverse techniquesincluding the use of evolutionary genetic algorithms [11][12][13] and neural networks [8] -have been proposed to compute the Gurson-Tvergaard-Needleman (GTN) [19,20] parameters from the load-displacement curve of unnotched SPT specimens. Void-based models have been particularly helpful in the development of new methodologies to estimate fracture toughness from SPT specimens [18].…”

Small punch creep test in a 316 austenitic stainless steel

“…This specimen is clamped in a fixture and punched, up to several millimeters, with a spherical indenter (Saucedo-Muñoz et al, 2003;Cuesta et al, 2010). The plastic deformation process of the material is characterized by monitoring the tip displacement of the specimen as a function of the applied force.…”