Modern Shoe Buckles from Archaeological Research in Gniew and Piaseczno (Pomerania Province, Poland)

During archaeological research carried out from 2009 to 2016 in the Church of St. Nicholas in Gniew, a set of three metal buckles was found. Then, in 2017, excavations were conducted in crypts of the Church of the Nativity of the Blessed Virgin Mary in the village of Piaseczno, in the Gniew District. Two other pairs of buckles were uncovered at this site. All the buckles found differ considerably. Thanks to this, one can get an impression that apart from holding the shoe on the foot, they also served decorative purposes. One can distinguish two main types of buckles: those made of iron and those made of a copper alloy. The latter, considering ornaments, could be more valuable than their iron counterparts. Regardless of the alloy used, manufacturing techniques differed, some of which were those used in the case of buckles from Gniew and Piaseczno: wire forging, cutting out of thick metal sheet, and folding thin metal sheet. On account of their jewellery-like character, this small collection of buckles discussed could be bequeathed, while most grave shoes were only fastened with tailor’s pins or put on the feet of the dead without fastening. This practice particularly concerned shoes with textile uppers, which mostly meant women’s shoes. It may suggest that the items in question were rather owned by men. The buckles described could be thus elements of the everyday attire. Issues connected with a formal and typological interpretation of the buckles found indicate interpretive problems faced by archaeologists dealing with these aspects of costume studies. Modern shoes, due to the scarcity of artefacts in archaeological collections, remain mysterious and puzzling objects.

Constitutive Model of Thin Metal Sheet in Bulging Test Considering Strain Gradient Hardening

The study of the size effect was one of the most important subjects in the field of micro-forming. To investigate the stress of the thin sheet in the bulging test with the second order size effect, a constitutive equation considering the strain gradient hardening was proposed. Based on the equation, the stress of the thin sheet during the bulging test was calculated by the finite element method. The bulging tests with various thicknesses of brass sheets and radiuses of punching balls were performed to verify the proposed equation. The results showed that the constitutive equation could capture the stress variations, while the simulation using the constitutive equation from the conventional theory of plasticity showed the results with large deviation from those of the experiment. It was found that the stress was sensitive to the thickness of the sheet and the radius of the punching ball in bulging test of thin brass sheet. The bulging of the thin brass sheet with a thickness below ten times of its material intrinsic length would cause the generation of the geometrically necessary dislocations, which induced the strain gradient hardening. Besides that, the decrement of the punching ball radius would also increase the inhomogeneous deformation and enhance the strain gradient hardening during the thin sheet bulging process. The strain gradient hardening during the thin sheet bulging test was related to the strain of the sheet. The hardening effect of the strain gradient was obvious when the strain was small. The strain gradient hardening should be considered in the thin sheet bulging test with the second order size effect.

Design of a Thin Metal Product with the Developable Middle Surface from a Sheet by Parabolic Bending

In the paper, the method to calculate the bending moments arising due to the process of parabolic bending of a thin metal sheet into a torso shell is offered. The problem is solved with the help of methods of differential geometry and shell theory. The possibility of manufacturing any torso product without creases and tears from a thin sheet made of plastic materials is theoretically proved. A review of experimental and theoretical works on pure bending is given. In contradistinction to the mathematical approach to bending a thin sheet into a torso shell (where the thickness of a sheet is assumed to be zero), this paper considers a technical approach taking into account the sheet thickness. It is shown that the normal stresses occurring in a thin sheet as a result of the bending can reach the yield point. On the contrary mathematical possibility to bend a sheet into a torso product, and then unbend it back into a flat position, it is shown in the paper that under certain conditions a sheet cannot be bent back to a flat sheet again due to the occurrence of plastic strains. The results of the research can be used in marine design, civil engineering, air-space industry, and other manufacturing processes.

Numerical Procedure for Identification of Constitutive Equations Based on Experimental Data

In this research experimental data obtained by well-known methods of displacement measurement are considered, whereas a thin cell meshwork has been fixed to the surface of the observed loaded object (thin metal sheet, for instance) and a set of point displacements has been ob- tained. Based on such experimental evidence, an eight point numerical procedure is proposed in the paper to identify the constitutive relations for small time increments. The presented approach is also applicable in case of micro deformations and facilitates the derivation of nonlinear constitutive equations in stress/strain increments. Approximate error es- timation of the procedure is additionally performed, and a test example is given.