Constitutive modeling of indentation cracking in fused silica

Bruns, Sebastian; Johanns, Kurt E.; Rehman, Hamad ur; Pharr, George M.; Durst, Karsten

doi:10.1111/jace.14734

Cited by 37 publications

(43 citation statements)

References 42 publications

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“…The indentation was repeated five times for each normal load of 2000 μN and 4000 μN. The measured average Young's modulus and hardness were 68.7 GPa and 9.43 GPa, respectively, as listed in Table , which fell in the reported ranges . The measured Young's modulus was close to that given by the product specification.…”

Section: Materials Properties and Indentation Experimentssupporting

confidence: 54%

A quantitative analysis of the indentation fracture of fused silica

Zhang

Sun

et al. 2019

J Am Ceram Soc

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It is unclear how the densification of fused silica influences the damage of its precision optics subjected to machining. This paper presents a quantitative analysis of the indentation fracture of fused silica involving densification with the embedded center of dilation (ECD) model. The Hertzian stress field and the ECD‐induced stress field were superposed to provide the overall stress distribution in the loading stage. A new method was established to accurately determine the strength of the ECD‐induced stress field with densification effects. With the aid of the ECD model, the starting locations, initiation stages and initiation sequence of crack morphologies were predicted by analyzing the stress fields. To quantitatively study the initiation of conical cracks in fused silica, the strain energy release rate was calculated by linear elastic fracture mechanics (LEFM). The predicted minimum threshold load leading to conical cracking was consistent with the measured values.

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Section: Materials Properties and Indentation Experimentssupporting

confidence: 54%

A quantitative analysis of the indentation fracture of fused silica

Zhang

Sun

et al. 2019

J Am Ceram Soc

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“…However, neither E, H, and m seem to change for different cooling rates. The amount of energy dissipated by densification reduces the amount of shear taking place, which reduces the probability for cracking as a smaller amount of residual stresses is introduced and maintained in the deformed volume (Kato et al, 2010;Gross, 2012;Sellappan et al, 2013;Bruns et al, 2017). This correlation is observed for impact and quasi-static indentation testing, both showing a larger threshold load for the activation of cracks for samples that were quenched than for annealed ones.…”

Section: Resultsmentioning

confidence: 78%

“…This means that an increasing cooling rate improves the crack resistance behavior. This is correlated to a larger amount of densification in the quenched sample compared to the furnace cooled one (Bruns et al, 2017). The crack probability study in this study (Figure 5) focuses on intermediate processing conditions, corresponding to a variation of the melt cooling temperature Tmc.…”

Section: Mechanical Properties Of Nbs2 Glasses With Different Networkmentioning

confidence: 99%

Influence of Cooling Rate on Cracking and Plastic Deformation during Impact and Indentation of Borosilicate Glasses

et al. 2017

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The influence of a changing glass topology on local mechanical properties was studied in a multitechnique nanomechanical approach. The glass response against sharp contacts can result in structural densification, plastic flow, or crack initiation. By using instrumented indentation testing, the mechanical response was studied in different strain rate regimes for a sodium borosilicate glass (NBS) exhibiting altering structures due to varying processing conditions. Comparison with data from former studies and with literature data on other glass structures helped to elucidate the role of the borate and silicate subnetworks and to understand the overall mechanical properties of the mixed glass systems. A peculiarity of some of the NBS glasses tested in this study is the fact that the connectivity of the borate and silicate entities depends on the sample's thermal history. Although the influence on macroscopic material properties such as E and H is minor, the onset of cracking indeed is influenced by those structural changes within the glass. Rapidly quenched glass shows an improved crack resistance, which is even more pronounced at high strain rates. Studies on various processing conditions further indicate that this transition is closely related to the cooling rate around Tg. The strain rate dependence of cracking is discussed in terms of the occurrence of shear deformation and densification.

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“…The shape of the cap is controlled by parameter R , the cap eccentricity, which forces the yield surface to be elliptical. It corresponds to the ratio of the hydrostatic yield strength p b to the yield strength under pure shear d. Further details on this constitutive description can be found elsewhere …”

Section: Resultsmentioning

confidence: 99%

Indentation densification of fused silica assessed by raman spectroscopy and constitutive finite element analysis

Bruns

Uesbeck²,

Fuhrmann

et al. 2020

J Am Ceram Soc

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Inelastic deformation of anomalous glasses manifests in shear flow and densification of the glass network; the deformation behavior during indentation testing is linked strongly to both processes. In this paper, the indentation densification field of fused silica is investigated using depth‐resolved Raman spectroscopy and finite element simulations. Through affecting the size of the indent, the normal load and the Raman laser spot size determine the spatial sampling resolution, leading to a certain degree of structural averaging. For appropriate combinations of normal load (indent size) and laser spot diameter, a maximum densification of 18.4% was found at the indent center. The indentation behavior was modeled by extended Drucker‐Prager‐Cap (DPC) plasticity, assuming a sigmoidal hardening behavior of fused silica with a densification saturation of 21%. This procedure significantly improved the reproduction of the experimental densification field, yielding a maximum densification of 18.2% directly below the indenter tip. The degree of densification was found to be strongly linked to the hydrostatic pressure limit below the indenter in accordance to Johnson's expanding cavity model (J. Mech. Phys. Solids, 18 (1970) 115). Based on the good overlap between FEA and Raman, an alternative way to extract the empirical correlation factor m, which scales structural densification to Raman spectroscopic observations, is obtained. This approach does not require the use of intensive hydrostatic compaction experiments.

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Constitutive modeling of indentation cracking in fused silica

Cited by 37 publications

References 42 publications

A quantitative analysis of the indentation fracture of fused silica

A quantitative analysis of the indentation fracture of fused silica

Influence of Cooling Rate on Cracking and Plastic Deformation during Impact and Indentation of Borosilicate Glasses

Indentation densification of fused silica assessed by raman spectroscopy and constitutive finite element analysis

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