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A dispersion of stiff and thin ('rigid line') inclusions (RLIs) in a matrix material may result beneficial for stiffening in the elastic range, but might be detrimental to strength, as material instabilities may be triggered by inclusions when the matrix is brought to a viscoplastic-damaging state. This dual role of RLIs is investigated by means of the embedded reinforcement model. Validated against available analytical predictions, this numerical model is employed to assess the roles of RLIs' orientation, interaction, volume fraction, and distribution, considering up to 1500 inclusions. When the matrix material deforms inelastically, RLIs produce stress concentrations that promote the nucleation of shear bands. These are characterized at collapse for many distributions of RLIs, showing that their effects range from almost negligible to a disrupting alteration of the dominant failure mechanism. In the latter case, it is shown that the dominant shear bands can be fragmented by RLIs into a mosaic of tiny localization bands. These results offer new insights into energy dissipation mechanisms of reinforced materials, as they are promoted or inhibited by the interactions of rigid line inclusions. [ABSTRACT FROM AUTHOR]

Abstract The formability of newly developed steel grades is a key parameter for their successful implementation in the car body. In the present work, the influence of the microstructure on formability during air bending is studied. First- and third-generation advanced high strength steels with tensile strengths above 1000 MPa are investigated, which exhibit a broad range of microstructural constituents (ferritic bainite, bainite, martensite, and retained austenite). Interrupted bending experiments are performed on two grades of dual phase and complex phase steels, respectively, in order to reveal the microscopic deformation and failure processes. The formability in hole expansion tests is determined and used as a measure for the resistance of the materials against crack formation. The macroscopic deformation behavior of the materials is taken into account by measuring the differential strain hardening exponent and performing finite element simulations of the air bending process. Advantages and disadvantages of various microstructural features are worked out, and it is explained why the first-generation dual phase steel exhibits the lowest and the third-generation complex phase steel the best formability during air bending. [ABSTRACT FROM AUTHOR]

In this paper, we consider a non-local stochastic parabolic equation that actually serves as a mathematical model describing the adiabatic shear banding formation phenomena in strained metals. We first present the derivation of the mathematical model. Then we investigate under which circumstances a finite-time explosion for this non-local stochastic partial differential equation, corresponding to shear banding formation, occurs. For that purpose, some results related to the maximum principle for this non-local stochastic partial differential equation are derived, and afterwards the Kaplan eigenfunction method is employed. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]