Search Results for elastic bending

Bending is a common metalworking operation to create localized deformation in sheets (or blanks), plates, sections, tubes, and wires. This article emphasizes on the bending of sheet metal along with some coverage on flanging. It informs that variations in the bending stresses cause springback after bending, and discusses the variables and their effects on springback, as well as the methods to overcome or counteract them. These methods include overbending, bottoming or setting, and stretch bending. The article provides information on elastic bending, non-cylindrical bending, elastic-plastic bending, and pure plastic bending. Sheet metal bendability is a critical factor in many forming operations. The article illustrates the derivation of two relevant bend-ductility equations.

A characteristic feature of bending is the inhomogeneous (nonuniform) nature of the deformation. Therefore, in a bent specimen, the strain and stress at a given point are dependent on the location of the point with respect to the neutral axis of the cross-sectional area of the specimen. This article discusses the stress-strain relationships, strain curvature, and stress-moment equations for elastic, noncylindrical, elastic-plastic, and pure plastic bending conditions. It also reviews the distribution of residual stress and springback.

Bend tests are conducted to determine the ductility or strength of a material. This article discusses the different bend tests with emphasis on test methods, apparatuses, procedures, specimen preparation, and interpretation and reporting of results. The types of bend tests discussed are bending ductility tests, bending strength tests (ASTM E 855), bend tests as per EN 12384 and JIS 3130, and computer-aided bending tests. The three standard bending strength tests are the cantilever beam bend test, the three-point bend test, and the four-point bend test. European Standard EN 12384 specifies a bend test to determine the modulus of elasticity in bending. Japanese Industrial Standard JIS 3130 specifies two tests to determine the elastic limit of spring plate or strip: the repeated deflection spring test and the moment type spring test.

This article defines performance indices in a formal way and specifies how they are derived. The performance indices for a light, strong tie and a light, stiff beam are presented. The article presents two case studies that illustrate the use of material indices, shape factors, and selection charts to select materials.

Springback refers to the elastically driven change of shape that occurs after deforming a body and then releasing it. This article presents an introduction to the concepts of springback simulation as well as recommendations for its practice in a metal forming setting of thin beams or sheets. It discusses bending with tension and more complex numerical treatments. The article addresses the limitations of the various assumptions followed in springback simulation. It provides a discussion on the design of dies and tooling using an assumed springback prediction capability.

This article is a compilation of terms related to mechanical testing and evaluation of metals, plastics, ceramics, and composites.

Sheet metal forming operations are so diverse in type, extent, and rate that no single test provides an accurate indication of the formability of a material in all situations. This article presents an overview of types of forming, formability problems, and principal methods of measuring deformation. It reviews the effect of materials properties and temperature on formability. The article provides a detailed discussion on the two major categories of formability tests such as the intrinsic test, including uniaxial tension testing, plane-strain tension testing, biaxial stretch testing, and simulative tests such as bending tests, stretching tests, the Ohio State University test, the drawing test, and stretch-drawing tests. It extends the correlation between simulative tests and materials properties using forming limit diagrams and circle grid analysis, and discusses the improvements to the forming limit diagram technology.

This article introduces the concepts of linear-elastic fracture mechanics (LEFM) and elastic-plastic fracture mechanics (EPFM). It reviews the fracture mechanics of ceramics and ceramic matrix composites (CMCs). The article describes some fracture toughness measurement techniques used on ceramics and CMCs: single edge notch bending, compact tension, double cantilever beam testing, chevron notch methods, and double torsion. It presents descriptions organized by their specimen types, and includes the advantages and disadvantages, as well as the experimental control schemes employed for each specimen type.

This article discusses stress relaxation testing on metallic materials, as covered by ASTM E 328. It reviews the two types of stress relaxation tests performed in tension, long-term and accelerated testing. The article illustrates load characteristics and data representation for stress relaxation testing used for the most convenient and common uniaxial tensile test. It concludes with information on compression testing, bend testing, torsion testing, and tests on springs.

An integral aspect of designing and material selection is the use of mechanical properties derived from various mechanical testing. This article introduces the basic concepts of mechanical design and its relation with the properties derived from various mechanical testings, namely, tensile, compressive, hardness, torsion and bend, shear load, shock, and fatigue and creep testings. It describes the design criteria for combined properties derived from each of the mechanical testing. The article concludes with a discussion on the effect of environment on the mechanical properties.

Tubing of any cross-sectional shape can be straightened by using various equipment and techniques. This article provides a discussion on principal factors that influence the procedures and tooling of tube straightening. It describes the tooling and application of different types of tube straightening techniques, namely, press straightening, parallel-roll straightening, two-roll rotary straightening, multiple-roll rotary straightening, and ovalizing in rotary straighteners.

This article focuses on the evaluation of mechanical properties of freestanding films and films adherent to their substrates. Common methods of testing freestanding films, including uniaxial tensile testing, uniaxial creep testing, biaxial testing, and beam-bending methods, are discussed. For films which are adherent to their substrates, indentation testing is used to evaluate hardness, creep, and strength.

Fracture toughness is an empirical material property that is determined by one or more of a number of standard fracture toughness test methods. This article describes the fracture toughness test methods in a chronological outline, beginning with the methods that use the linear-elastic parameter. After this, the methods that use the nonlinear parameters are discussed. The article reviews some of the work in progress to update the standard test methods, namely, common fracture toughness test method and transition fracture toughness test method. Finally, an overview of fracture toughness testing for ceramic and polymer materials is provided.