The equation of a contour and the form factor of a hysteresis loop

Fomichev, P. A.; Trubchanin, I. Yu.

doi:10.1007/bf02767439

Strength Mater

1997

DOI: 10.1007/bf02767439

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The equation of a contour and the form factor of a hysteresis loop

P. A. Fomichev

I. Yu. Trubchanin

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Cited by 3 publications

(7 citation statements)

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“…The main conclusion following from those investigations is that in the low-cycle fatigue region the n 1 value does not vary [55,61], whereas in transition to the high-cycle fatigue [48,53,55] the hysteresis loop shape changes and the n 1 value increases that, in accordance with (16), leads to a decrease in K sh . It was shown [53] that, with a decrease in the stress amplitude from 400 to 250 MPa, the n 1 value for a carbon steel increases from 0.15 to 0.4 with a large scatter in the results being observed.…”

supporting

confidence: 68%

“…The results of the investigations into the variation of the coefficient of the hysteresis loop shape K sh and, accordingly, the coefficient of the hysteresis loop contour n 1 [48,55,61] depending on the plastic strain amplitude per cycle are ambiguous.…”

mentioning

confidence: 95%

“…According to [45][46][47], formula (7) yields a relationship for determining the hysteresis loop area in the form or, in accordance with [10,48], in the form…”

mentioning

confidence: 99%

“…Quite a number of works are known where the studies were focused on the variation of the coefficient of the hysteresis loop contour n 1 for metals and alloys of various classes depending on the influence of high or low temperatures [49,56], heat treatment and structure [56][57][58], inhomogeneity of the billet properties [59], strain rate [60], number of load cycles [55], plastic strain amplitude [48,53,55,61], and other factors. The resulting numerical values of n 1 lie generally within the ranges indicated in Table 1.…”

mentioning

confidence: 99%

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Nonlocalized Fatigue Damage of Metals and Alloys. Part 1. Inelasticity, Investigation Methods, and Results

Troshchenko

2005

Strength Mater

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Analysis of data presented in the literature and results of unique studies revealed that nonlocalized fatigue damage of metals and alloys, which manifests itself in the initiation and propagation of a large number of microcracks distributed arbitrarily in the bulk of the material, can be considered with the use of the characteristics of inelastic deformation such as inelastic strain and inelastic strain energy per cycle. The author studied the nature of the material inelasticity and methods of its investigation. Analysis has been made of the hysteresis loop shape, width, and area, as well as of the main regularities of inelastic deformation of metals and alloys.Keywords: nonlocalized fatigue damage, inelastic strain, inelastic strain energy.Introduction. The process of fatigue of metals and alloys can be divided into two stages: the stage of nonlocalized fatigue damage and that of localized fatigue damage where the process of fatigue is defined by the propagation of the dominant crack that leads to final fracture.As numerous investigations showed, the stage of the fatigue crack initiation is longer lasting than the stage of its propagation. Figure 1 shows the results of generalization of some of those investigations performed in [1], which are presented in the form of the relation between the ratio of the number of cycles to the initiation of a fatigue crack of length about 0.05 mm under axial loading of smooth specimens from various materials to the number of cycles to fracture and the number of cycles to fracture.It is seen that under high-cycle fatigue, which corresponds to the number of cycles to fracture equal to 10 5 and more, the stage of the fatigue crack initiation accounts for more than 90% of the total number of cycles to fracture.In the case of the fatigue fracture in the presence of stress concentration, fretting, etc., the stage of crack initiation is of shorter duration, yet it remains dominating.The size of a fatigue crack corresponding to the transition from the stage of nonlocalized to the stage of localized fatigue damage depends on the material structure, the level of acting stresses, loading regime, stress state type, and other factors. The size of such a crack generally decreases with increasing strength of the alloy and increases in torsion as compared with tension-compression [2,3].Thus, in [3] for steel 45 (σ u = 516 MPa) it is shown that, at stresses equal to the fatigue limit for the test duration 10 7 cycles, the size of the maximum crack in tension-compression and in torsion is 0.05 and 0.17 mm, respectively, and for 12KhN3A steel of higher strength (σ u = 950 MPa), it is 0.03 and 0.08, respectively. These crack dimensions are close to those used for plotting the relation in Fig. 1.

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supporting

confidence: 68%

mentioning

confidence: 95%

“…According to [45][46][47], formula (7) yields a relationship for determining the hysteresis loop area in the form or, in accordance with [10,48], in the form…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Nonlocalized Fatigue Damage of Metals and Alloys. Part 1. Inelasticity, Investigation Methods, and Results

Troshchenko

2005

Strength Mater

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“…where K f is the hysteresis loop form factor [9] which for aluminum alloys varies insignificantly and can be taken constant, K f = 3. 4.…”

mentioning

confidence: 99%

Substantiation of the predicted fatigue curve for structural elements of aluminum alloy

Fomichev

2011

Strength Mater

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The paper provides a more specific definition of the method for calculating fatigue life of aluminum alloy structural elements by a local stress-strain state in pulsating regular loading. The calculated results are compared to the test data for specimens with a free and filled holes and for lugs. Recommendations on the method application for calculating fatigue life by nominal stresses are given.Introduction. The method for calculating fatigue life by nominal stresses [1] is based on experimental fatigue curves for specimens with a free hole. These specimens with a ratio between the width and hole diameter B d = 6 have been standardized in aircraft industry. The stress concentration factor in elastic deformation is 2.6 for net stresses and 3.12 for gross stresses. The gross stresses are found without allowing for weakening of the specimen cross section near the hole. The hole diameter depends on the fasteners to be used and is usually 6 to 8 mm. Standard plate specimens were tested by means of a testing machine with pulsating loading. The fatigue curve plotted by the test results is called the basic curve. The fatigue life of structural elements is calculated by using an effective stress concentration factor which is determined either experimentally or by empirical relations based on test results for specimens with a free hole or for lugs. In specimens with a hole, the stress concentration is due to the stresses that pass round the hole. For lugs a contact problem of interaction between the bolt and the specimen is realized; a load is transmitted to the specimen via bearing stresses, the maximum stresses arise at the contact arc break points. The tests are performed until the specimen fails, and a relation between the number of cycles and the maximum nominal stress is found. The fatigue curves are approximated by exponential equations.The method of the fatigue life calculation by a local stress-strain state (SSS), which is based on the energy criterion for fatigue failure [2][3][4], makes it possible to theoretically predict the fatigue life till the formation of microcracks on the hole surface and macrocracks in the stress concentrator. For input data on the material properties this method uses cyclic deformation and fatigue characteristics as determined from the test results for smooth specimens.The objective of the present work is to specify the method for calculating fatigue life of aluminum alloy structural elements by the local SSS under pulsating regular loading and to provide recommendations for the method application to fatigue life calculation by normal stresses.The Method for Fatigue Life Calculation by Local SSS. The analysis for the pulsating regular loading case consists in the following.1. The Calculation of Local Notch-Tip Stresses and Strains at Maximum Nominal Stress s n max in a Loading Cycle. The local stress can be found through the solution of a nonlinear deformation problem by the finite-element method or by the refined Neuber formula [5]

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The coefficient of transverse strain and strain hysteresis under cyclic loading

Fomichev¹,

Trubchanin²

1997

Strength Mater

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The equation of a contour and the form factor of a hysteresis loop

Cited by 3 publications

References 1 publication

Nonlocalized Fatigue Damage of Metals and Alloys. Part 1. Inelasticity, Investigation Methods, and Results

Nonlocalized Fatigue Damage of Metals and Alloys. Part 1. Inelasticity, Investigation Methods, and Results

Substantiation of the predicted fatigue curve for structural elements of aluminum alloy

The coefficient of transverse strain and strain hysteresis under cyclic loading

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