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elastic-plastic bending
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Book Chapter
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005161
EISBN: 978-1-62708-186-3
...-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. bendability bending bending stress elastic bending elastic-plastic bending flanging non...
Abstract
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.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003262
EISBN: 978-1-62708-176-4
.... 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. stress-strain behavior bending deformation strain...
Abstract
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.
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005131
EISBN: 978-1-62708-186-3
... of large-strain, elastic-plastic deformation are treated in a simplified, intuitive way, with numerous references provided for those wishing to delve into the theoretical underpinnings in more detail. Simple bending is first considered, along with a discussion of approximations, then bending with tension...
Abstract
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.
Image
Published: 01 January 2006
Fig. 7 Springback of a beam in simple bending. (a) Elastic bending. (b) Elastic and plastic bending. (c) Bending and stretching
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Image
Published: 01 January 2006
Fig. 24 Simulated role of plasticity in springback for a draw-bend test. (a) Difference of springback angle (Δθ) for pure-elastic and elastoplastic springback simulations. (b) Differences in through-thickness stress distribution following pure-elastic and elastoplastic springback. R / t
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Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.9781627081931
EISBN: 978-1-62708-193-1
Book Chapter
Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0005723
EISBN: 978-1-62708-193-1
... to maximum load, Tmax maximum temperature in a cycle LEFM linear elastic fracture mechanics R = crmin /crmax, or R = (1-A)l(l +A) rcp cyclic plastic zone radius Tmin minimum temperature in a cycle M bending moment M(T) center-cracked tension specimen rP rotation factor in CTOD test, plastic TEM transmission...
Book Chapter
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0005689
EISBN: 978-1-62708-176-4
... below ductile fracture. Fracture characterized by tear- elastic calibration device. A device for use in which a material can presumably endure an ing of metal accompanied by appreciable verifying the load readings of a testing ma- infinite number of stress cycles. The value of gross plastic deformation...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.9781627081764
EISBN: 978-1-62708-176-4
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003311
EISBN: 978-1-62708-176-4
... specimen type. linear-elastic fracture mechanics elastic-plastic fracture mechanics fracture mechanics ceramics single edge notch bending testing compact tension testing double cantilever beam testing chevron notch methods double torsion method fracture toughness ceramic matrix composites...
Abstract
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.
Book Chapter
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005169
EISBN: 978-1-62708-186-3
... in elastic region, where x1 is b Materials derivative (denotes rate of eu the bending ber direction. For atomic percent DASA change) exp B atmospheres (pressure) plane strain and isotropic bal American Welding Society DBMS day f bcc DBTT incremental strain F elasticity, E0= E : bct Burgers (slip) vector...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003290
EISBN: 978-1-62708-176-4
... the yield stress on loading. Whether or not there is permanent plastic strain on loading, there is an elastic strain that, in linear elastic materials, is proportional to the stress through the appropriate temperature sensitive modulus. If the temperature and stress are sufficiently high creep will occur...
Abstract
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.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003306
EISBN: 978-1-62708-176-4
... Evaluation From these test results, J is evaluated from the load-versus-loadline displacement record. The J is calculated from a linear combination of an elastic term and a plastic term given as: (Eq 7) J = J e1 + J p 1 K 2 ( 1 − ν 2 ) E + η p1 B...
Abstract
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.
Book: Surface Engineering
Series: ASM Handbook
Volume: 5
Publisher: ASM International
Published: 01 January 1994
DOI: 10.31399/asm.hb.v05.a0001297
EISBN: 978-1-62708-170-2
... used in the technique described above were vibrated electrostatically, and Young's modulus was obtained from the observed natural frequency ( Ref 10 ). The beam-bending method is well suited for the determination of elastic and some plastic properties of freestanding films. The principal drawback...
Abstract
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.
Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002380
EISBN: 978-1-62708-193-1
.... The CTOD standard uses the same bend and compact specimens that are used in the J Ic test; thus the same loading fixtures are used. The method requires measurement of load and displacement during the test. The formulas for δ calculation use a combination of an elastic and a plastic component for δ...
Abstract
This article describes the test methods of fracture toughness, namely, linear-elastic and nonlinear fracture toughness testing methods. Linear-elastic fracture toughness testing includes slow and rapid loading, crack initiation, and crack arrest method. Nonlinear testing comprises J IC testing, J-R curve evaluation, and crack tip opening displacement (CTOD) method. Other methods used include the combined J standard method, the common fracture toughness test, transition fracture toughness testing, and the weldment fracture testing method.
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005163
EISBN: 978-1-62708-186-3
... σ 0 R E · t × 100 where σ 0 is the tensile yield stress, E is elastic modulus, and t is thickness. A higher-order term occurs for elastic-perfectly plastic springback (Eq 12 and 13 in the article “Springback” in this Volume), but this additional term is not a significant...
Abstract
This article provides information on the classification of high-strength steels (HSS) and advanced high-strength steels (AHSS) and tabulates designation of HSS and AHSS as recommended by the American Iron and Steel Institute. It reviews the major grades of HSS and AHSS that are used or will potentially be used in industrial applications. The article discusses different stamping issues such as edge cracking and springback, encountered during forming of AHSS, and lists guidelines for reducing springback in stamped components. It concludes with a discussion on the major advantages and disadvantages of using HSS and AHSS in automotive applications.
Image
Published: 01 January 2006
Fig. 10 Effect of sheet tension on springback for an elastic, perfectly plastic constitutive equation for low-strength steel. (a) Constant thickness. (b) Changing thickness. r , radius of curvature after springback; R , radius of primary bending curvature; t , sheet thickness; E , Young's
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Image
Published: 30 November 2018
Fig. 8 Effect of sheet tension on springback for an elastic, perfectly plastic constitutive equation for low-strength steel. (a) Constant thickness. (b) Changing thickness. r, radius of curvature after springback; R, radius of primary bending curvature; t, sheet thickness; E, Young's modulus
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Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003314
EISBN: 978-1-62708-176-4
..., and the range of plastic strain is used as a measure of the severity of fatigue “loading.” On the other hand, cracks begin to appear quite late in cyclic life (90–99%) in the very low-strain, elastically dominated, high-cycle life regime. There is a gradual transition between these two extremes of behavior...
Abstract
This article describes the phenomena of crack initiation and early growth. It examines specimen design and preparation as well as the apparatus used in crack initiation testing. The article provides descriptions of the various commercially available fatigue testing machines: axial fatigue testing machines and bending fatigue machines. Load cells, grips and alignment devices, extensometry and strain measuring devices, environmental chambers, graphic recorders, furnaces, and heating systems of ancillary equipment are discussed. The article presents technologies available to accomplish closed loop control of materials testing systems in performing standard materials tests and for the development of custom testing applications. It explores the advanced software tools for materials testing. The article includes a description of baseline isothermal fatigue testing, creep-fatigue interaction, and thermomechanical fatigue. The effects of various variables on fatigue resistance and guidelines for fatigue testing are also presented.
Book Chapter
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003241
EISBN: 978-1-62708-199-3
... stress to a design engineer, resistance to scratching to a mineralogist, and resistance to cutting to a machinist. Although these various definitions of hardness appear to differ significantly in character, they are all related to the plastic flow stress of the material. Table 1 lists the major...
Abstract
This article reviews the various types of mechanical testing methods, including hardness testing; tension testing; compression testing; dynamic fracture testing; fracture toughness testing; fatigue life testing; fatigue crack growth testing; and creep, stress-rupture, and stress-relaxation testing. Shear testing, torsion testing, and formability testing are also discussed. The discussion of tension testing includes information about stress-strain curves and the properties described by them.
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