Ratchet Boundary for Superimposed Biaxial Membrane Stress States

2018 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Thermal Expansion ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Pressure Vessels ◽  
Stress Fields ◽  
Design Codes ◽  
Bending Stress ◽  
Membrane Stress ◽  
Asme Code ◽  
Stress States

Thermal membrane and bending stress fields exist where the thermal expansion of pressure vessel components is constrained. When such stress fields interact with pressure stresses in a shell, ratcheting can occur below the ratchet boundary indicated by the Bree diagram that is implemented in the design Codes. The interaction of primary and thermal membrane stress fields with arbitrary biaxiality is not implemented presently in the thermal stress ratchet rules of the ASME Code, and is examined in this paper. An analytical solution for the ratchet boundary is derived based on a non-cyclic method that uses a generalized static shakedown theorem. The solutions for specific applications in pressure vessels are discussed, and a comparison with the interaction diagrams for specific cases that can be found in the literature is performed.

On the Interaction of Thermal Membrane and Thermal Bending Stress in Shakedown Analysis

2008 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Thermal Stress ◽  
Bending Stress ◽  
Membrane Stress ◽  
Secondary Stress ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Thermal Bending ◽  
Asme Code ◽  
The Impact ◽  
Current Code

When the primary plus secondary stress range exceeds 3 Sm, the current ASME Code rules on simplified elastic-plastic analysis impose two separate requirements to evaluate the potential for ratcheting. The range of primary plus secondary stress excluding thermal bending must be less than 3 Sm, and the thermal stress must satisfy the Bree criterion for thermal stress ratchet. It has been shown previously that this method can be unconservative, i.e. predict shakedown when elastic-plastic analysis shows ratcheting. This paper clarifies the interaction between thermal membrane and bending stress in the presence of a primary membrane stress. An analytical model is used to derive the closed-form ratchet boundary for combined uniform loading of this type. The impact of having stress gradients along the wall that are typical for discontinuities is studied numerically. Simple modifications of the current Code methods are suggested that would achieve a clearer and better-justified set of rules.

Ratcheting With No Thermal Bending and Membrane Stress

2016 ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Thermal Stress ◽  
Thermal Loading ◽  
Mechanical Load ◽  
Failure Mechanisms ◽  
Extreme Case ◽  
Cyclic Stress ◽  
Maximum Temperature ◽  
Bending Stress ◽  
Thermal Bending ◽  
Stress States

The ASME B&PV Code provides design by analysis rules that address failure mechanisms under cyclic loading. One of these potential failure mechanisms is incremental plastic collapse, or ratcheting. Miller presented the technical basis for the present Code requirements in a technical paper in 1959. Miller’s equations for the ratchet boundary address a beam under a cyclic through-thickness thermal gradient acting together with a steady axial mechanical load. This ratchet boundary applies approximately to a pressurized cylinder with through-thickness thermal bending stress. Conditions arise sometimes in practice where cooling or heating is applied simultaneously to the inner and outer surface of pressure boundary. The extreme case of such a scenario arises when both surfaces experience the same thermal condition such that there is a cyclic thermal stress but both zero membrane thermal stress and zero thermal bending stress The question is, could ratcheting occur in this case? This paper derives the ratchet boundary for cases when the maximum temperature occurs mid-way through the thickness. The linearized stress due to thermal loading is zero. The solution is obtained using FE analysis and the Non-Cyclic Method (NCM) that has been proposed previously by the authors. The NCM is a generalization of the static shakedown theorem and allows the ratchet boundary to be calculated for both elastic and elastic-plastic cyclic stress states.

ASME Code Evaluation on Stress Analysis of Snubber

2006 ◽  
Vol 326-328 ◽  
pp. 1339-1342
Author(s):  
Sun Chul Huh ◽  
Han Shik Chung ◽  
Hyo Min Jeong ◽  
Byeong Keun Choi
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Bending Stress ◽  
Membrane Stress ◽  
Commercial Program ◽  
Asme Code ◽  
Bending Stresses ◽  
Live Loads ◽  
Design Value ◽  
Design Optimum

Small snubber of hydrogen compressor do duty as buffer pulsation of compressed hydrogen. Snubber is a kind of internal pressure vessel and design optimum of snubber very important problem. In this paper, we will estimation results of elastic finite element structural analysis using the commercial program such as ANSYS for comparison to the limits in ASME Code Sec. Ⅷ that are related to membrane and bending stresses. In case of membrane stress in a circular cylindrical due to internal pressure or to distributed live loads. Bending stress in the central portion of flat head due to pressure. In addition, We will propose optimum design value of snubber for hydrogen compressor.

The Shakedown Boundary for Parabolic Stress Distribution in NB-3222.5

2013 ◽  
Author(s):  
W. Reinhardt ◽  
A. Asadkarami
Keyword(s):  
Thermal Stress ◽  
Temperature Distribution ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Thermal Loading ◽  
Exact Analytical Solution ◽  
Second Order ◽  
Fe Model ◽  
Membrane Stress ◽  
Shakedown Analysis

The rules for the prevention of thermal stress ratchet in NB-3222.5 address the interaction of general primary membrane stress with two types of cyclic thermal loading. The first is a linear through-wall temperature gradient, for which the shakedown boundary is given by the well-known Bree diagram. The Code provides a second shakedown boundary for the interaction of general primary membrane stress with a “parabolic” temperature distribution. The corresponding ratchet boundary is fully defined in the elastic range, but only three points are given in the elastic-plastic regime. The range of validity of this ratchet boundary in terms of the thermal stress distribution (does “parabolic” mean second-order in the thickness coordinate or any polynomial of degree greater than one? If it is second-order, are there any further restrictions?) is not well defined in NB-3222.5. Using a direct lower bound method of shakedown analysis, the non-cyclic method, an exact analytical solution is derived for the shakedown boundary corresponding to the interaction of general primary membrane stress with a cyclic “parabolic” temperature distribution. By comparison to what is given in NB-3222.5, the thermal condition for which the Code equation is valid is defined and its range of validity is established. To study the transition behavior to the steady state and to confirm the analytical solution, numerical results using an FE model are also obtained.

Shakedown at Thermal Discontinuities Involving Thermal Membrane and Thermal Bending Stress

2012 ◽  
Author(s):  
Ali Asadkarami ◽  
Wolf Reinhardt
Keyword(s):  
Thermal Stress ◽  
Stress Gradient ◽  
Axial Direction ◽  
Bending Stress ◽  
Primary Stress ◽  
Perfectly Plastic ◽  
Thermal Bending ◽  
Asme Code ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

The current ASME Code Section III NB-3200 rules on thermal stress ratchet require that the thermal stress must be less than the ratchet condition that Bree established for a cyclic pure thermal bending stress as a function of the level of primary membrane stress. It has been shown that this method can predict shakedown when elastic-perfectly plastic analysis shows ratcheting. However, there is also conservatism in the Code rules because the highest stresses that dominate the evaluation of a component are typically found at discontinuities, where there is a stress gradient at least in the axial direction. The stress limits, on the other hand, are based on stress distributions that are constant in the axial (and circumferential) direction. This paper investigates the effect of thermal discontinuities on the shakedown limit in the presence of a thermal through-wall gradient and a pressure-induced primary stress. The investigation is based on the simple model of a cylinder with an isolated thermal discontinuity. The effect of proximity to another discontinuity is explored, to obtain the minimum distance between two discontinuities that would allow them to be considered separately. Simple rules are developed and proposed to take potentially advantage of higher stress limits at an isolated discontinuity.

Revisiting the Bree Diagram

2016 ◽  
Author(s):  
Daniel W. Spring ◽  
Charles Panzarella ◽  
David A. Osage
Keyword(s):  
Thermal Stress ◽  
Axial Stress ◽  
Pressure Vessels ◽  
Operating Conditions ◽  
Plastic Behavior ◽  
Membrane Stress ◽  
Incremental Growth ◽  
Simplifying Assumptions ◽  
Thin Walled ◽  
Made In

As early as the 1950’s, practitioners observed progressive distortion in thin-walled pressure vessels subjected to a constant axial stress and a cyclic thermal stress. In the late 1960’s, Bree [1] developed a theory and corresponding diagram plotting the primary membrane stress versus the cyclic thermal stress which delineates the various zones of plastic behavior. The zones include elastic cycling, plastic cycling, elastic cycling after initial plasticity, and ratcheting leading to incremental growth. This paper revisits the original Bree problem and investigates many of the recent advancements made to alleviate several of the simplifying assumptions Bree made in developing the diagram, to bring it in line with more modern operating conditions. In particular, a novel modification to the Bree diagram to account for the ratio of the yield stress at the operating extremums is proposed. This paper also reviews some advancements made to incorporate creep into the problem and discusses the operating conditions wherein creep effects may be significant. The outcomes of this paper will help expand the applicability of the Bree diagram, broadening its scope to encompass operating conditions more representative of modern applications.

Distinguishing Ratcheting and Shakedown Conditions in Pressure Vessels

2003 ◽  
Author(s):  
W. Reinhardt
Keyword(s):  
Thermal Stress ◽  
Kinematic Hardening ◽  
Pressure Vessels ◽  
Stress Range ◽  
Secondary Stress ◽  
Hardening Models ◽  
Asme Code ◽  
Elastic Shakedown

The nature of the boundary between stable cycling and ratcheting is discussed using several illustrative example scenarios. The examples are analyzed in the context of the elastic methods currently in the ASME Code to demonstrate the conservatism of the existing approach that exists in some cases, and the unconservative estimation that exists in others. It is shown that the limit on the linearized primary plus secondary stress range can be related to conditions for elastic shakedown in certain kinematic hardening models of plasticity, while the limits on thermal stress ratchet address only scenarios similar to the Bree problem.

scholarly journals Out-of-Plane Thermal Expansion Coefficient and Biaxial Young’s Modulus of Sputtered ITO Thin Films

Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 153
Author(s):  
Chuen-Lin Tien ◽  
Tsai-Wei Lin
Keyword(s):  
Thin Films ◽  
Thermal Expansion ◽  
Thermal Stress ◽  
Young’S Modulus ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Young's Modulus ◽  
Heating Temperature ◽  
Glass Substrates ◽  
Ito Thin Films

This paper proposes a measuring apparatus and method for simultaneous determination of the thermal expansion coefficient and biaxial Young’s modulus of indium tin oxide (ITO) thin films. ITO thin films simultaneously coated on N-BK7 and S-TIM35 glass substrates were prepared by direct current (DC) magnetron sputtering deposition. The thermo-mechanical parameters of ITO thin films were investigated experimentally. Thermal stress in sputtered ITO films was evaluated by an improved Twyman–Green interferometer associated with wavelet transform at different temperatures. When the heating temperature increased from 30 °C to 100 °C, the tensile thermal stress of ITO thin films increased. The increase in substrate temperature led to the decrease of total residual stress deposited on two glass substrates. A linear relationship between the thermal stress and substrate heating temperature was found. The thermal expansion coefficient and biaxial Young’s modulus of the films were measured by the double substrate method. The results show that the out of plane thermal expansion coefficient and biaxial Young’s modulus of the ITO film were 5.81 × 10−6 °C−1 and 475 GPa.

scholarly journals Unravelling thermal stress due to thermal expansion mismatch in metal–organic frameworks for methane storage

2021 ◽  
Author(s):  
Jelle Wieme ◽  
Veronique Van Speybroeck
Keyword(s):  
Thermal Expansion ◽  
Thermal Stress ◽  
Pressure Coefficient ◽  
Metal Organic Frameworks ◽  
Methane Storage ◽  
Thermal Expansion Mismatch ◽  
Thermal Pressure ◽  
Temperature Changes ◽  
Metal Organic ◽  
The Impact

Thermal stress is present in metal–organic frameworks undergoing temperature changes during adsorption and desorption. We computed the thermal pressure coefficient as a proxy for this phenomenon and discuss the impact of thermal expansion mismatch.

Determination of Stress Intensity Factors for Gradient Stress Fields

1977 ◽  
Vol 99 (3) ◽  
pp. 477-484 ◽  
Author(s):  
J. M. Bloom ◽  
W. A. Van Der Sluys
Keyword(s):  
Stress Intensity ◽  
Crack Length ◽  
Stress Intensity Factors ◽  
Maximum Stress ◽  
Nuclear Industry ◽  
Stress Fields ◽  
Polynomial Method ◽  
Intensity Factors ◽  
Asme Code ◽  
Linear Envelope

This paper evaluates eight different analytical procedures used in determining elastic stress intensity factors for gradient or nonlinear stress fields. From a fracture viewpoint, the main interest in this problem comes from the nuclear industry where the safety of the nuclear system is of concern. A fracture mechanics analysis is then required to demonstrate the vessel integrity under these postulated accident conditions. The geometry chosen for his study is that of a 10-in. thick flawed plate with nonuniform stress distribution through the thickness. Two loading conditions are evaluated, both nonlinear and both defined by polynomials. The assumed cracks are infinitely long surface defects. Eight methods are used to find the stress intensity factor: 1–maximum stress, 2–linear envelope, 3–linearization over the crack length from ASME Code, Section XI, 4–equivalent linear moment from ASME Code, Section III, Appendix G for thermal loadings, 5–integration method from WRC 175, Appendix 4 for thermal loadings, 6–8-node singularity (quarter-point) isoparametric element in conjunction with the displacement method, 7–polynomial method, and 8–semi-infinite edge crack linear distribution over crack. Comparisons are made between all eight procedures with the finding that the methods can be ranked in order of decreasing conservatism and ease of application as follows: 1–maximum stress, 2–linear envelope, 3–linearization over the crack length, 4–polynomial method, and 5–singularity element method. Good agreement is found between the last three of these methods. The remaining three methods produce nonconservative results.

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