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David Arencón Osuna, Marcelo de Sousa Pais Antunes, Vera Cristina de Redondo Realinho, José Ignacio Velasco
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linear elastic deformation
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Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006941
EISBN: 978-1-62708-395-9
...-versus-time graph can be constructed from creep data. As long as the material remains within the linear viscoelastic range, the modulus calculated from creep data will be a function of time alone. The contributions to the instantaneous deformation are a recoverable elastic strain and a permanent plastic...
Abstract
This article describes the viscoelastic behavior of plastics in their solid state only, from the standpoint of the material deforming without fracturing. The consequences of viscoelasticity on the mechanical properties of plastics are described, especially in terms of time-dependencies, as well as the dependence of the viscoelastic character of a plastic on chemical, physical, and compositional variables. By examining the viscoelastic behavior of plastics, the information obtained are then applied in situations in which it may be important to anticipate the long-term properties of a material. This includes assessing the extent of stress decay in materials that are pre-stressed, the noise and vibration transmission characteristics of a material, the amount of heat build-up in a material subjected to cyclic deformation, and the extent a material can recover from any prior deformation. Several qualitative graphs are presented, which highlights the possible differences in the viscoelastic behavior that can exist among plastics.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... mechanics analysis linear elastic fracture mechanics analysis stress analysis equations stress analysis THE STRESSES acting on a component may cause unacceptable deformation, cracking, or fracture. By definition, after a stress-related failure has occurred, it is a given that the stresses reached...
Abstract
This article describes concepts and tools that can be used by the failure analyst to understand and address deformation, cracking, or fracture after a stress-related failure has occurred. Issues related to the determination and use of stress are detailed. Stress is defined, and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear elastic fracture mechanics analysis, with some mention of elastic-plastic fracture mechanics analysis. The article describes the probabilistic aspects of fatigue and fracture. Information on crack-growth simulation of the material is also provided.
Book Chapter
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006910
EISBN: 978-1-62708-395-9
... Abstract There are many different types of polymeric materials, ranging from glassy to semicrystalline polymers and even blends. Their mechanical properties range from pure elastic with very high strains to fracture (elastomers) to almost pure linear elastic (Hookian behavior) with low strains...
Abstract
There are many different types of polymeric materials, ranging from glassy to semicrystalline polymers and even blends. Their mechanical properties range from pure elastic with very high strains to fracture (elastomers) to almost pure linear elastic (Hookian behavior) with low strains to fracture (glassy polymers). This article provides an overview of historical development of fracture behavior in polymers. It discusses the processes involved in three fracture test methods for polymers, namely linear elastic fracture mechanics, elastic-plastic fracture mechanics, and post-yield fracture mechanics.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006919
EISBN: 978-1-62708-395-9
... of a component to failure due to stresses applied at high rates. The two most significant concepts in this definition are those of failure due to mechanical stress and high rates of loading. Failure of a plastic component can take many forms. There are situations in which excessive elastic deformation...
Abstract
This article reviews the impact response of plastic components and the various methods used to evaluate it.. It describes the effects of loading rate on polymer deformation and the influence of temperature and strain rate on failure mode. It discusses the advantages and limitations of standard impact tests, the use of puncture tests for assessing material behavior under extreme strain, and the application of fracture mechanics for analyzing impact failures. It also develops and demonstrates the theory involved in the design and analysis of thin-walled, injection-molded plastic components.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003513
EISBN: 978-1-62708-180-1
... δ e δ mat FAD, failure assessment diagram; LEFM, linear elastic fracture mechanics; EPFM, elastic-plastic fracture mechanics; CTOD, crack-tip opening displacement; FAC, failure assessment curve; FAP, failure assessment point; J e , elastic component of J -integral; J p...
Abstract
Optimized modeling of fracture-critical structural components and connections requires the application of elastic-plastic fracture mechanics. Such applications, however, can require sophisticated analytical techniques such as crack tip opening displacement (CTOD), failure assessment diagram (FAD), and deformation plasticity failure assessment diagram (DPFAD). This article presents the origin and description of FAD and addresses R6 FAD using J-integral. It details the fracture criteria of BS 7910. The factors to be considered during the use of FAD and the applications of FAD are also reviewed.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
... The transformations A and B can be combined by defining C = BA . In that case T ′ ′ = C T C T which is in the same form as the single transformation. Stress and strain in an isotropic body for elastic deformation are related by linear expressions that result from Hooke's law...
Abstract
This article describes the underlying fundamentals, applications, the relevance and necessity of performing proper stress analysis in conducting a failure analysis. It presents an introduction to the stress analysis of bodies containing crack-like imperfections and the topic of fracture mechanics. The fracture mechanics approach is an important part of stress analysis at the tips of sharp cracks or discontinuities. The article reviews fracture mechanics concepts, including linear elastic fracture mechanics, elastic-plastic fracture mechanics, and subcritical fracture mechanics. It also provides information on the applications of fracture mechanics in failure analysis.
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001766
EISBN: 978-1-62708-241-9
... that the anchor rod was loaded beyond its installation limit of 6,000 ft-lbf based upon the underlying assumption that 6,000 ft-lbf was the elastic limit of the screw anchor. While in many applications, the onset of bulk plastic deformation is considered to constitute failure of a component, it is not true...
Abstract
During the installation of power transmission lines across a major interstate highway, a temporary anchor stabilizing one of the poles failed, resulting in the loss of the pole and the associated power lines. It also contributed to a single vehicle incident on the adjacent roadway. Post-failure analysis revealed that the fracture was precipitated by a preexisting weld-related crack. Closed form and numerical stress analyses were also conducted, with the results indicating that the anchor was installed properly within the parameters intended by the manufacturer.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006934
EISBN: 978-1-62708-395-9
... of applying a constant stress to a material specimen and recording its deformation (strain) over time. When an ideal elastic solid is stressed, an immediate strain is recorded, and the applied stress, σ, is directly proportional to the strain, ε. The elastic behavior is described by the familiar Hooke...
Abstract
This article describes the general aspects of creep, stress relaxation, and yielding for homogeneous polymers. It then presents creep failure mechanisms in polymers. The article discusses extrapolative methods for the prediction of long-term creep failure in polymer materials. Then, the widely used models to simulate the service life of polymers are highlighted. These include the Burgers power-law model, the Findley power-law model, the time-temperature superposition (or equivalence) principle (TTSP), and the time-stress superposition principle (TSSP). The Larson-Miller parametric method, one of the most common to describe the material deformation and rupture time, is also discussed.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006918
EISBN: 978-1-62708-395-9
... are most appropriate for characterizing crack growth in polymers or the nature of crack-growth resistance in a polymer under specific test conditions. The main analyses used in the characterization of crack growth are linear elastic ( K -based) or elastic-plastic ( J -based) fracture processes ( Ref 13...
Abstract
This article reviews generalized test methodologies for fatigue characterization of polymers and examines fatigue fracture mechanisms in different engineering plastics. It provides detailed micromechanistic images of crack-tip processes for a variety of semicrystalline and amorphous engineering polymers. The article describes fracture mechanics solutions and approaches to the fatigue characterization of engineering polymers when dealing with macroscale fatigue crack growth. It includes mechanistic images for high-density polyethylene, ultrahigh-molecular-weight polyethylene, nylon 6, 6, polycarbonate, and polypropylene. The article describes the micromechanisms of toughening of plastics and uses a macroscale approach of applying fracture mechanics to the fatigue life prediction of engineering polymers, building on the mechanistic concepts. It also describes the factors affecting fatigue performance of polymers.
Book Chapter
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003541
EISBN: 978-1-62708-180-1
... a critical value, K Ic , for the plane-strain fracture toughness, which is considered to be a material property ( Ref 22 ). Linear elastic fracture mechanics properties per ASTM D5045 are appropriate for highly cross-linked thermosets or glassy thermoplastics incapable of significant plastic deformation...
Abstract
This article reviews the mechanical behavior and fracture characteristics that discriminate structural polymers from metals. It provides information on deformation, fracture, and crack propagation as well as the fractography involving the examination and interpretation of fracture surfaces, to determine the cause of failure. The fracture modes such as ductile fractures and brittle fractures are reviewed. The article also presents a detailed account of various fracture surface features. It concludes with several cases of field failure in various polymers that illustrate the applicability of available analytical tools in conjunction with an understanding of failure mechanisms.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006865
EISBN: 978-1-62708-395-9
... to be a material property ( Ref 14 ). Linear elastic fracture mechanics properties ( Ref 22 ) are appropriate for highly cross-linked thermosets or glassy thermoplastics incapable of significant plastic deformation (e.g., polystyrene). Unlike shear yielding, which occurs at constant volume, craze yielding...
Abstract
This article reviews the mechanical behavior and fracture characteristics that discriminate structural polymers from metals, including plastic deformation. It provides overviews of crack propagation and fractography. The article presents the distinction between ductile and brittle fracture modes. Several case studies of field failure in various polymers are also presented to illustrate the applicability of available analytical tools in conjunction with an understanding of failure mechanisms.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006928
EISBN: 978-1-62708-395-9
... are derived, which describe the balance between elasticity, viscosity, and energy absorption. Standard methods are given in ISO 6721 and ASTM D5023 to D5026. Because dynamic properties are usually measured with small deformations, they involve only relative displacement of polymer segments in the linear...
Abstract
This article briefly introduces some commonly used methods for mechanical testing. It describes the test methods and provides comparative data for the mechanical property tests. In addition, creep testing and dynamic mechanical analyses of viscoelastic plastics are also briefly described. The article discusses the processes involved in the short-term and long-term tensile testing of plastics. Information on the strength/modulus and deflection tests, impact toughness, hardness testing, and fatigue testing of plastics is also provided. The article describes tension testing of elastomers and fibers. It covers two basic methods to test the mechanical properties of fibers, namely the single-filament tension test and the tensile test of a yarn or a group of fibers.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006930
EISBN: 978-1-62708-395-9
..., angular velocity On the other hand, pure deformation, which is appropriate for describing how solids behave (elastic behavior), is denoted by a spring in rheology textbooks. The behavior exhibited by solids is shown in Fig. 2 , which shows that for solids, the force exerted by the operator...
Abstract
Rheology is defined as the study of the flow and deformation of matter. This article begins with an examination of flow behavior. It describes the geometries and methods employed for rheological testing of polymers in their molten state. It also discusses materials that are predominantly in the solid state and the methods employed for solids testing. Examples of unidirectional and dynamic oscillatory testing are provided for different mechanical behaviors.
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001762
EISBN: 978-1-62708-241-9
... a microscope. The pre-existing crack morphology was intergranular fracture in the axles studied. An estimate of the force required to cause the axle fracture can be made using the measured crack size, fracture toughness determined from these tests, and linear elastic fracture mechanics. The axle can...
Abstract
Rollover accidents in light trucks and cars involving an axle failure frequently raise the question of whether the axle broke causing the rollover or did the axle break as a result of the rollover. Axles in these vehicles are induction hardened medium carbon steel. Bearings ride directly on the axles. This article provides a fractography/fracture mechanic approach to making the determination of when the axle failed. Full scale tests on axle assemblies and suspensions provided data for fracture toughness in the induction hardened outer case on the axle. These tests also demonstrated that roller bearing indentions on the axle journal, cross pin indentation on the end of the axle, and axle bending can be accounted for by spring energy release following axle failure. Pre-existing cracks in the induction hardened axle are small and are often difficult to see without a microscope. The pre-existing crack morphology was intergranular fracture in the axles studied. An estimate of the force required to cause the axle fracture can be made using the measured crack size, fracture toughness determined from these tests, and linear elastic fracture mechanics. The axle can be reliably said to have failed prior to rollover if the estimated force for failure is equal to or less than forces imposed on the axle during events leading to the rollover.
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001851
EISBN: 978-1-62708-241-9
... be derived by the finite element method with the introduction of consistent variables to satisfy the geometric compatibility at the internal boundaries. Motion of the rotating shaft can be described as a Euler beam, while motion of the spinning disk results in elastic deformation and departure from a rigid...
Abstract
Shaft misalignment and rotor unbalance contribute to the premature failure of many machine components. To understand how these failures occur and quantify the effects, investigators developed a model of a rotating assembly, including a motor, flexible coupling, driveshaft, and bearings. Equations of motion accounting for misalignment and unbalance were then derived using finite elements. A spectral method for resolving these equations was also developed, making it possible to obtain and analyze dynamic system response and identify misalignment and unbalance conditions.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003526
EISBN: 978-1-62708-180-1
... of general-purpose FEA software programs. It is also very useful when performing failure analyses, because failure and fracture of materials often involve some form of plastic deformation before failure. Most analyses start out as linear elastic problems. The results of a linear analysis can indicate whether...
Abstract
This article provides information on the development of finite element analysis (FEA) and describes the general-purpose applications of FEA software programs in structural and thermal, static and transient, and linear and nonlinear analyses. It discusses special-purpose finite element applications in piping and pressure vessel analysis, impact analysis, and microelectronics. The article describes the steps involved in the design process using the FEA. It concludes with two case histories that involve the use of FEA in failure analysis.
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
... produces slip lines in the crystals of a metal, which develop into small cracks. These small cracks then propagate, coalesce, and result in an eventual fracture that usually involves no gross plastic deformation and generally occurs at stress levels below the material yield strength. Consequently, at one...
Abstract
This article offers an overview of fatigue fundamentals, common fatigue terminology, and examples of damage morphology. It presents a summary of relevant engineering mechanics, cyclic plasticity principles, and perspective on the modern design by analysis (DBA) techniques. The article reviews fatigue assessment methods incorporated in international design and post construction codes and standards, with special emphasis on evaluating welds. Specifically, the stress-life approach, the strain-life approach, and the fracture mechanics (crack growth) approach are described. An overview of high-cycle welded fatigue methods, cycle-counting techniques, and a discussion on ratcheting are also offered. A historical synopsis of fatigue technology advancements and commentary on component design and fabrication strategies to mitigate fatigue damage and improve damage tolerance are provided. Finally, the article presents practical fatigue assessment case studies of in-service equipment (pressure vessels) that employ DBA methods.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006944
EISBN: 978-1-62708-395-9
.... Figure 6 shows the effect of temperature on the stress-strain of cellulose acetate ( Ref 10 ). Deviation of the linearity in the elastic region is observed clearly at all temperatures, and yielding occurs. As the temperature is increased, the stress levels for deformation decrease, the elongation...
Abstract
The discussion on the fracture of solid materials, both metals and polymers, customarily begins with a presentation of the stress-strain behavior and of how various conditions such as temperature and strain-rate affect the mechanisms of deformation and fracture. This article describes crazing and fracture in polymeric materials, with a review of the behavior of the elastic modulus as a function of temperature or time parameters, emphasizing the importance of the viscoelastic nature of their deformation and fracture. The discussion covers the behavior of polymers under stress, provides information on ductile and brittle behaviors, and describes craze initiation in polymers and crack formation and fracture by crazing. Macroscopic permanent deformation of polymeric materials caused by shear-yielding and crazing, which eventually can result in fracture and failure, is also covered.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006781
EISBN: 978-1-62708-295-2
... plastic behavior ( Ref 11 , 12 ): (Eq 12) da dN = C Δ J q e ( − Q p RT ) Equation 11 estimates the fatigue crack growth per cycle, da / dN , as a function of material- and environmental-specific constants a and b ; the linear elastic stress-intensity factor...
Abstract
Thermomechanical fatigue (TMF) is the general term given to the material damage accumulation process that occurs with simultaneous changes in temperature and mechanical loading. TMF may couple cyclic inelastic deformation accumulation, temperature-assisted diffusion within the material, temperature-assisted grain-boundary evolution, and temperature-driven surface oxidation, among other things. This article discusses some of the major aspects and challenges of dealing with TMF life prediction. It describes the damage mechanisms of TMF and covers various experimental techniques to promote TMF damage mechanisms and elucidate mechanism coupling interactions. In addition, life modeling in TMF conditions and a practical application of TMF life prediction are presented.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006773
EISBN: 978-1-62708-295-2
... form of plastic deformation before failure. Most analyses start out as linear elastic problems. The results of a linear analysis can indicate whether stresses in the component exceed the yield strength of the material and give an indication of the size of the high-stress plastic zone. In many cases...
Abstract
When complex designs, transient loadings, and nonlinear material behavior must be evaluated, computer-based techniques are used. This is where the finite-element analysis (FEA) is most applicable and provides considerable assistance in design analysis as well as failure analysis. This article provides a general view on the applicability of finite-element modeling in conducting analyses of failed components. It highlights the uses of finite-element modeling in the area of failure analysis and design, with emphasis on structural analysis. The discussion covers the general development and both general- and special-purpose applications of FEA. The special-purpose applications of FEA covered are piping and pressure vessel analysis, impact analysis, and microelectronic and microelectromechanical systems analysis. The article provides case histories that involved the use of FEA in failure analysis.
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