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Paris law
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in Service Lifetime Assessment of Polymeric Products
> Characterization and Failure Analysis of Plastics
Published: 15 May 2022
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006921
EISBN: 978-1-62708-395-9
... the hydrostatic design basis approach, Miner's rule, the Arrhenius model, and the Paris Law for fatigue crack propagation, are discussed. accelerated testing Arrhenius model chemical degradation environmental stress cracking fatigue crack propagation Miner's rule Paris law polymeric materials...
Abstract
The lifetime assessment of polymeric products is complicated, and if the methodology utilized leads to inaccurate predictions, the mistakes could lead to financial loss as well as potential loss of life, depending on the service application of the product. This article provides information on the common aging mechanisms of polymeric materials and the common accelerated testing methods used to obtain relevant data that are used with the prediction models that enable service life assessment. Beginning with a discussion of what constitutes a product failure, this article then reviews four of the eight major aging mechanisms, namely environmental stress cracking, chemical degradation, creep, and fatigue, as well as the methods used in product service lifetime assessment for them. Later, several methods of service lifetime prediction that have gained industry-wide acceptance, namely the hydrostatic design basis approach, Miner's rule, the Arrhenius model, and the Paris Law for fatigue crack propagation, are discussed.
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Published: 01 January 2002
Fig. 42 Fatigue crack propagation rate versus stress intensity factor range. Fatigue striations may be present on the fracture surface for loading in the linear portion of the curve (Paris Law region), and permit analytical estimations of life to fracture. Just as fracture toughness varies
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Published: 15 January 2021
Fig. 43 Fatigue crack propagation rate ( da / dN ) versus stress-intensity factor range (Δ K ). Fatigue striations may be present on the fracture surface for loading in the linear portion of the curve (Paris law region) and permit analytical estimations of life to fracture. Just as fracture
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Published: 01 June 2024
Fig. 17 Effect of orientation on stage II (Paris regime) fatigue crack-growth rate using the Paris law parameters measured on strongly textured Ti-6Al-4V sheet. The orientations represent (hkil) || cracking plane and [uvtw] || crack-growth direction. Courtesy of Dr. M.C. Brandes. Source: Ref
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Image
Published: 01 December 1998
Fig. 10 Schematic representation of fatigue crack propagation behavior. In regime I, the crack-growth rate is low because the threshold for crack propagation is approached. In regime II, the Paris law is obeyed, while in regime III, the crack-growth rate increases above that predicted
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Image
Published: 01 January 1996
Fig. 10 Schematic representation of fatigue crack propagation behavior. In regime I the crack growth rate is low since the threshold for crack propagation is approached. In regime II the so-called Paris law is obeyed while in regime III the crack growth rate increases above that predicted
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Image
Published: 01 December 2009
Fig. 1 Schematic of log crack-growth rate ( da / dN) versus log applied stress-intensity factor range (Δ K ) showing the decreasing crack-growth rate region (I), the linear (or Paris law) region (II), and the accelerating region (III)
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005416
EISBN: 978-1-62708-196-2
... extension per cycle ( da / dN ) becomes measurable at a threshold Δ K th , followed by the slower extension rate in the Paris Law regime ( Ref 9 , Ref 10 , Ref 11 , Ref 12 ) described by the proportionality (Eq 6) log Δ K ∝ log { d a d N } m where da / dN...
Abstract
Neural networks permit the discovery of fundamental relationships and quantitative structure within vast arrays of ill-understood data. This article provides an overview of neural network modeling method, describing its overfitting nature. It discusses the use of neural networks in modeling noise and uncertainties in conducting experiments. The article also presents examples of the application of neural-network modeling to the behavior of metals.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005419
EISBN: 978-1-62708-196-2
... defined as the Δ K that produces a crack-growth rate of 1 × us;10 m/cycle ( Ref 6 ). The linear region (in log-log space), region II, is called the Paris law or power law region, because Paul Paris first noted that a power law would fit the crack-growth rate data in this region ( Ref 8 ). That is: (Eq...
Abstract
Understanding fatigue crack growth is critical for the safe operation of many structural components. This article reviews the standard fracture mechanics and methods to determine the crack growth rate for a material and loading condition experimentally. It also addresses the two most important aspects of crack-growth modeling: loading environment and crack geometry.
Book: Composites
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003382
EISBN: 978-1-62708-195-5
... mechanics analysis. The dominant mechanism leading to failure in metals is crack growth. The Paris law , which is a primary tool to predict flaw growth in metals, relates the rate of growth of a macrocrack to the change in stress-intensity factor induced by the loading. The Paris law is written in the form...
Abstract
In the design of composite structures for durability and damage tolerance, the primary concerns are out-of-plane failures, such as delamination, material degradation associated with environment, stability under compression loading, large degree of scatter in fatigue life, and bearing failure of joints. This article presents an introductory discussion on the fatigue damage process, methodologies assessing fatigue behavior, and life prediction models. It describes the damage mechanisms introduced for a quasi-isotropic laminate under tension-compression fatigue loading. Delamination is a critical issue in fatigue and generally results from high interlaminar normal and shear stresses. The article schematically illustrates the structural elements in which high interlaminar stresses are common. It concludes with a discussion on the classification of fatigue models such as mechanistic or phenomenological, for composite materials under cyclic loading.
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002476
EISBN: 978-1-62708-194-8
Abstract
Brittle materials, such as ceramics, intermetallics, and graphites, are increasingly being used in the fabrication of lightweight components. This article focuses on the design methodologies and characterization of certain material properties. It describes the fundamental concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength. The article discusses the two-parameter and three-parameter Weibull distribution for representing the underlying probability density function for tensile strength. It reviews life prediction reliability models used for predicting the life of a component with complex geometry and loading. The article outlines reliability algorithms and presents several applications to illustrate the utilization of these reliability algorithms in structural applications.
Book: Composites
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003380
EISBN: 978-1-62708-195-5
...) Because delaminations often form and grow under cyclic loads, a fatigue characterization is also desired. The classical Paris law for fatigue crack growth (which describes crack growth per load cycle as a function of the range in the stress- intensity factor) has often been generated ( 13 , 14 15...
Abstract
Delamination is one of the most commonly observed failure modes in composite materials. This article describes the three fundamental fracture failure modes of composite delamination, namely, opening, in-plane shearing, and tearing or scissoring shearing modes. It discusses the characterization and analysis of delamination. The article also reviews the prediction of delamination factors, such as flexbeam fatigue life, and skin/stiffener pull-off strength and life.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003328
EISBN: 978-1-62708-176-4
... as follows: Δ K = f ( Δ σ , a , f ) The crack propagation rate da / dN for Δ K -values greater than the threshold value Δ K th can be calculated by the well-known Paris law ( Ref 35 ), which has the general form: d a / d N = C ( Δ K ) m...
Abstract
This article provides an overview of the safety aspects and integrity concept for pressure vessels, piping, and tubing. It focuses on the fracture mechanics approaches used to validate components with longitudinal cracks and circumferential cracks and to analyze crack growth behavior under cyclic loading. Full-scale testing facilities and the typical test results required for various applications are discussed. The article also presents information on the transferability of mechanical properties of materials.
Book: Composites
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003468
EISBN: 978-1-62708-195-5
... of river marks growing from those reinforcement particles that are visible on the fracture surface. The regions between the plateaus are characterized by shear steps. Striations are visible on the fracture surface of the SiC-reinforced composite ( Fig. 4a ). As Δ K increases into the Paris Law region [1...
Abstract
This article describes the fatigue properties of particle-reinforced metal-matrix composites (PR-MMCs) in terms of mechanisms of crack initiation, fatigue life, and fatigue crack growth. It reviews specimen preparation and microscopic procedures that are used in fatigue testing of MMCs. It also describes the evaluation of the long fatigue crack growth behavior of MMCs by using the test methods and specimens that are used for unreinforced metallic alloys. Fractography of MMCs under plane-strain conditions is also described with information on the observed features of MMC fatigue fracture surfaces and their observation methods.
Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002351
EISBN: 978-1-62708-193-1
... used forms of Eq 3 is the Paris equation, which is used to describe crack growth behavior over a fairly broad range of Δ K . Equation 3 then takes on the specific form: (Eq 4) d a d N = C ( Δ K ) n where C and n are material parameters that depend on temperature...
Abstract
This article reviews the basic processes of fracture and fatigue and shows how these processes occur in materials. It presents an overview of the fatigue mechanisms and some related models for appropriate classes of materials, such as carbon and alloy steels, aluminum alloys, and titanium alloys. Microstructural factors that affect the fracture toughness of these materials, are discussed. The article describes fatigue crack propagation (FCP) mechanisms and related models. It also analyzes FCP behavior in these materials, with an emphasis on general microstructural factors.
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001477
EISBN: 978-1-62708-173-3
... the propagation of a fatigue crack from the inherent discontinuities that exist at the weld toe and the weld root. Fracture mechanics also can be used to predict the life of a joint with a weld discontinuity. The most widely accepted fatigue crack growth relationship is the Paris law ( Ref 15 ), which can...
Abstract
Fitness-for-service assessment procedures can be used to assess the integrity, or remaining life, of components in service. Depending on the operating environment and the nature of the applied loading, a structure can fail by a number of different modes: brittle fracture, ductile fracture, plastic collapse, fatigue, creep, corrosion, and buckling. This article focuses on the broad categories of these failure modes: fracture, fatigue, environmental cracking, and high-temperature creep. It also discusses the benefits of a fitness-for-service approach.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003537
EISBN: 978-1-62708-180-1
Abstract
This article provides an overview of fractography and explains how it is used in failure analysis. It reviews the basic types of fracture processes, namely, ductile, brittle, fatigue, and creep, principally in terms of fracture appearances, such as microstructure. The article also describes the general features of fatigue fractures in terms of crack initiation and fatigue crack propagation.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006940
EISBN: 978-1-62708-395-9
... qualitative in nature yet significantly important. A thermodynamic approach ( Ref 83 ) treats the phenomenon as local instability and proposes a framework to establish the law of crack initiation. However, a quantitative measure of the initiation time from a smooth-bar specimen is currently still not possible...
Abstract
Failure of structural polymeric materials under cyclic application of stress or strain is a subject of industrial importance. The understanding of fatigue mechanisms (damage) and the development of constitutive equations for damage evolution, leading to crack initiation and propagation as a function of loading or displacement history, represent a fundamental problem for scientists and engineers. This article describes the approaches to predict fatigue life and discusses the difference between thermal and mechanical fatigue failure of polymers.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006774
EISBN: 978-1-62708-295-2
Abstract
Engineering component and structure failures manifest through many mechanisms but are most often associated with fracture in one or more forms. This article introduces the subject of fractography and aspects of how it is used in failure analysis. The basic types of fracture processes (ductile, brittle, fatigue, and creep) are described briefly, principally in terms of fracture appearances. A description of the surface, structure, and behavior of each fracture process is also included. The article provides a framework from which a prospective analyst can begin to study the fracture of a component of interest in a failure investigation. Details on the mechanisms of deformation, brittle transgranular fracture, intergranular fracture, fatigue fracture, and environmentally affected fracture are also provided.
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