Research Of The Effect Of T-stress On Fracture Problem In Quasicrystals Of A Cruciform Crack With Unequal Arms

A solid structure possessing quasi-periodic translational symmetry and non-crystallographic rotational symmetry was first observed in the electron diffraction pattern of an alloy of Al-Mn by Shechtman in 1984.This new solid structure was defined as quasicrystals.In the early fracture mechanics theory,the stress intensity factor,which is the singular term in the Williams characteristic series expansion.It was considered to play a dominant role in the stress and displacement fields at the tip of the linear elastic crack,and the stress intensity factor was often regarded as the only parameter determining the stress field at the tip of the crack.However,many studies in the 1970 s and1980s found that the effect of the non-singular constant term in the Williams expansion on the fracture behavior of the material is not negligible.In this paper,the associated boundary value problems can transform to a system of singular integral equations by using the integral transformation technique,and discussing the effect of T-stress on the fracture in an infinite two-dimensional decagonal quasicrystals,two-dimensional decagonal piezoelectric quasicrystals,and cubic quasicrystals of a cruciform crack with unequal arms.Chapter 1,the background,significance and status of quasicrystal and T-stress research,as well as the main research methods and contents of this paper are introduced.Chapter 2,the T-stress near the tips of a cruciform crack with unequal arms in the two-dimensional decagonal quasicrystals are analyzed.The associated boundary value problems can transform to a system of singular integral equations by using the integral transformation technique.T-stresses of phonon field and phason field can be expressed as the sum of an integral involving crack opening displacements and applied loading at infinity.crack opening displacements play a leading role in determining T-stresses of phonon field and phason field.The role of the T-stresses in brittle fracture for two-dimensional decagonal quasicrystals is emphasized.The effect of stress on two-dimensional decagonal quasicrystals in brittle fracture is discussed by numerical calculations,as well as the analysis of the special case of cross-crossing cracks into single cracks with the same crack arm length.Chapter 3,T-stress near the tips of a cruciform crack with unequal arms in the two-dimensional decagonal piezoelectric quasicrystals is analyzed.In order to derive the values of T-stresses of phonon field and phason field at the crack tips,the integral transformation technique is adopted,which is similar to the determining of the stress intensity factors,using the integral transformation technique,the values of T-stresses of phonon field and phason field at the crack tips is derived,T-stresses can be expressed as a sum of an integral involving crack opening displacement and applied loading at infinity.Especially when the two arm lengths are close to each other,the effect of crack opening displacement on the T-stress is not negligible.After numerical analysis,it can be found that the T-stress of with electric field is greater than that of the no electric field in two-dimensional decagonal piezoelectric quasicrystals,Meanwhile,the T-stress of with phason field is greater than that of the with phason field in two-dimensional decagonal piezoelectric quasicrystals,indicating that the phason field has a perturbing effect on the T-stress of two-dimensional decagonal piezoelectric quasicrystals.Chapter 4,the T-stress near the tips of a cruciform crack with unequal arms in the cubic quasicrystals is analyzed.First,using the integral transformation technique,the values of the stress intensity factors and T-stresses of phonon field and phason field at the crack tips is derived,T-stresses can be expressed as a sum of an integral involving crack opening displacement and applied loading at infinity.Obtained results indicate that,crack opening displacement plays a leading role in determining T-stress.Moreover,the influence of the ratio of two crack-arm lengths b/a and the crack opening displacement on the T-stress of a cruciform crack is examined.if the phason field is absent,it is in agreement with the one derived for a cruciform crack with unequal arms in elastic.