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At least 19 records

Proof Mate: An Interactive Proof Helper for PVS (Tool Paper)

This paper presents Proof Mate, an interactive proof helper for the PVS verification system. The helper is integrated in VSCode-PVS, the Visual Studio Code extension for PVS. It extends the capabilities of VSCode-PVS by introducing new functionalities for suggesting proof commands, sketching proof attempts, and repairing broken proofs during interactive proof sessions. This work further aligns VSCode-PVS to the functionalities provided by modern development tools, with the ultimate aim to facilitate the adoption of formal methods in engineering practices and education.

Interactive Theorem Proving

Proof Mate: An Interactive Proof Helper for PVS

This paper presents Proof Mate, an interactive proof helper for the PVS verification system. The helper is integrated in VSCode-PVS, the Visual Studio Code extension for PVS. It extends the capabilities of VSCode-PVS by introducing new functionalities for suggesting proof commands, sketching proof attempts, and repairing broken proofs during interactive proof sessions. This work further aligns VSCode-PVS to the functionalities provided by modern development tools, with the ultimate aim to facilitate the adoption of formal methods in engineering practices and education.

Formal Methods

Evaluation of the concept of pressure proof testing fuselage structures

The FAA and NASA have recently completed independent technical evaluations of the concept of pressure proof testing the fuselage of commercial transport airplanes. The results of these evaluations are summarized. The objectives of the evaluations were to establish the potential benefit of the pressure proof test, to quantify the most desirable proof test pressure, and to quantify the required proof test interval. The focus of the evaluations was on multiple-site cracks extending from adjacent rivet holes of a typical fuselage longitudinal lap splice joint. The FAA and NASA do not support pressure proof testing the fuselage of aging commercial transport aircraft. The argument against proof testing is as follows: (1) a single proof test does not insure an indefinite life; therefore, the proof test must be repeated at regular intervals; (2) for a proof factor of 1.33, the required proof test interval must be below 300 flights to account for uncertainties in the evaluation; (3) conducting the proof test at a proof factor of 1.5 would considerably exceed the fuselage design limit load; therefore, it is not consistent with accepted safe practices; and (4) better safety can be assured by implementing enhanced nondestructive inspection requirements, and adequate reliability can be achieved by an inspection interval several times longer than the proof test interval.

Harris, Charles E.

Significant issues in proof testing: A critical appraisal

Issues which impact on the interpretation and quantification of proof test benefits are reviewed. The importance of each issue in contributing to the extra quality assurance conferred by proof testing components is discussed, particularly with respect to the application of advanced fracture mechanics concepts to enhance the flaw screening capability of a proof test analysis. Items covered include the role in proof testing of elastic-plastic fracture mechanics, ductile instability analysis, deterministic versus probabilistic analysis, single versus multiple cycle proof testing, and non-destructive examination (NDE). The effects of proof testing on subsequent service life are reviewed, particularly with regard to stress redistribution and changes in fracture behavior resulting from the overload. The importance of proof test conditions are also addressed, covering aspects related to test temperature, simulation of service environments, test media and the application of real-time NDE. The role of each issue in a proof test methodology is assessed with respect to its ability to: promote proof test practice to a state-of-the-art; aid optimization of proof test design; and increase awareness and understanding of outstanding issues.

Chell, G. G.

Proof Testing Aluminum and Titanium Thin-Walled Tubes for Aerospace Applications

Proof testing aerospace components aids in verifying the structural integrity of flight hardware. This process is often an important step in the certification process for critical parts. Though proof testing is a common practice at NASA and in industry, there is often a need to understand better the effectiveness of proof testing pressure systems discovering cracklike flaws or defects. Often proof tests are used in requirements and in practice as technical rationale for screening critical defects in a part in lieu of performing a non-destructive inspection. The intent of this work is to define proof test failure envelopes for thin-walled tubes composed of two materials: aluminum and titanium. Both materials are common in aerospace thin-walled tubing applications which is why these were the materials chosen for this study. The fracture mechanics software NASGRO was used to perform a parametric study on the effect of defects in thin-walled tubes subjected to proof testing. For both materials, the parameters varied in the NASGRO analyses were aspect ratio, proof test pressure, thickness, diameter, and flaw multiplier. With each case defined as a through crack or failure, the results were then pulled into MATLAB in order to parse through the data and produce failure envelope plots. Failure envelopes were created by meshing a surface in between the minimum proof pressure failing data points. As expected, based on material properties, the plots indicated the aluminum material would fail at much lower proof tests than the titanium. The parametric data and failure envelopes may be used as general qualitative insight on the effectiveness of proof testing thin-walled tubes of similar alloys.

Leah B Davis

An evaluation of the pressure proof test concept for thin sheet 2024-T3

The concept of pressure proof testing of fuselage structures with fatigue cracks to insure structural integrity was evaluated from a fracture mechanics viewpoint. A generic analytical and experimental investigation was conducted on uniaxially loaded flat panels with crack configurations and stress levels typical of longitudinal lap splice joints in commercial transport aircraft fuselages. The results revealed that the remaining fatigue life after a proof test was longer than that without the proof test because of crack growth retardation due to increased crack closure. However, based on a crack length that is slightly less than the critical value at the maximum proof test stress, the minimum assured life or proof test interval must be no more than 550 pressure cycles for a 1.33 proof factor and 1530 pressure cycles for a 1.5 proof factor to prevent in-flight failures.

Dawicke, D. S.

An evaluation of the pressure proof test concept for thin sheet 2024-T3

The concept of pressure proof testing of fuselage structures with fatigue cracks to insure structural integrity was evaluated from a fracture mechanics viewpoint. A generic analytical and experimental investigation was conducted on uniaxially loaded flat panels with crack configurations and stress levels typical of longitudinal lap-splice joints in commercial transport aircraft fuselage. The results revealed that the remaining fatigue life after a proof test was longer than that without the proof test because of crack growth retardation due to increased crack closure. However, based on a crack length that is slightly less than the critical value at the maximum proof test stress, the minimum assured life or proof test interval must be no more than 550 pressure cycles for a 1.33 proof factor and 1530 pressure cycles for a 1.5 proof factor to prevent in-flight failures.

Dawicke, D. S.

Proof test and fatigue crack growth modeling on 2024-T3 aluminum alloy

Pressure proof testing of aircraft fuselage structures has been suggested as a means of screening critical crack sizes and of extending their useful life. The objective of this paper is to study the proof-test concept and to model the crack-growth process on a ductile material. Simulated proof and operational fatigue life tests have been conducted on cracked panels made of 2024-T3 aluminum alloy sheet material. A fatigue crack-closure model was modified to simulate the proof test and operational fatigue cycling. Using crack-growth rate and resistance-curve data, the model was able to predict crack growth during and after the proof load. These tests and analyses indicate that the proof test increases fatigue life; but the beneficial life, after a 1.33 or 1.5 proof, was less than a few hundred cycles.

Newman, J. C., Jr.

An evaluation of the pressure proof test concept for 2024-T3 aluminium alloy sheet

The concept of pressure proof testing of fuselage structures with fatigue cracks to insure structural integrity was evaluated from a fracture mechanics viewpoint. A generic analytical and experimental investigation was conducted on uniaxially loaded flat panels with crack configurations and stress levels typical of longitudinal lap splice joints in commercial transport aircraft fuselages. The results revealed that the remaining fatigue life after a proof cycle was longer than that without the proof cycle because of crack growth retardation due to increased crack closure. However, based on a crack length that is slightly less than the critical value at the maximum proof stress, the minimum assured life or proof test interval must be no more than 550 pressure cycles for a 1.33 proof factor and 1530 pressure cycles for a 1.5 proof factor to prevent in-flight failures.

Dawicke, D. S.

NASA Contractor Report: Guidelines for Proof Test Analysis

These Guidelines integrate state-of-the-art Elastic-Plastic Fracture Mechanics (EPFM) and proof test implementation issues into a comprehensive proof test analysis procedure in the form of a Road Map which identifies the types of data, fracture mechanics based parameters, and calculations needed to perform flaw screening and minimum proof load analyses of fracture critical components. Worked examples are presented to illustrate the application of the Road Map to proof test analysis. The state-of-the-art fracture technology employed in these Guidelines is based on the EPFM parameter, J, and a pictorial representation of a J fracture analysis, called the Failure Assessment Diagram (FAD) approach. The recommended fracture technology is validated using finite element J results, and laboratory and hardware fracture test results on the nickel-based superalloy IN-718, the aluminum alloy 2024-T351 1, and ferritic pressure vessel steels. In all cases the laboratory specimens and hardware failed by ductile mechanisms. Advanced proof test analyses involving probability analysis and Multiple Cycle Proof Testing (MCPT) are addressed. Finally, recommendations are provided on to how to account for the effects of the proof test overload on subsequent service fatigue and fracture behaviors.

Chell, G. G.

Guidelines for Proof Test Analysis

These guidelines integrate state-of-the-art elastic-plastic fracture mechanics (EPFM) and proof test implementation issues into a comprehensive proof test analysis procedure in the form of a road map which identifies the types of data, fracture mechanics based parameters, and calculations needed to perform flaw screening and minimum proof load analyses of fracture critical components. Worked examples are presented to illustrate the application of the road map to proof test analysis. The state-of-the art fracture technology employed in these guidelines is based on the EPFM parameter, J, and a pictorial representation of a J fracture analysis, called the failure assessment diagram (FAD) approach. The recommended fracture technology is validated using finite element J results, and laboratory and hardware fracture test results on the nickel-based superalloy Inconel 718, the aluminum alloy 2024-T3511, and ferritic pressure vessel steels. In all cases the laboratory specimens and hardware failed by ductile mechanisms. Advanced proof test analyses involving probability analysis and multiple-cycle proof testing (MCPT) are addressed. Finally, recommendations are provided on how to account for the effects of the proof test overload on subsequent service fatigue and fracture behaviors.

Chell, G. G.

Deriving Safety Cases from Automatically Constructed Proofs

Formal proofs provide detailed justification for the validity of claims and are widely used in formal software development methods. However, they are often complex and difficult to understand, because the formalism in which they are constructed and encoded is usually machine-oriented, and they may also be based on assumptions that are not justified. This causes concerns about the trustworthiness of using formal proofs as arguments in safety-critical applications. Here, we present an approach to develop safety cases that correspond to formal proofs found by automated theorem provers and reveal the underlying argumentation structure and top-level assumptions. We concentrate on natural deduction style proofs, which are closer to human reasoning than resolution proofs, and show how to construct the safety cases by covering the natural deduction proof tree with corresponding safety case fragments. We also abstract away logical book-keeping steps, which reduces the size of the constructed safety cases. We show how the approach can be applied to the proofs found by the Muscadet prover.

Basir, Nurlida

Accounting for Proof Test Data in a Reliability Based Design Optimization Framework

This paper investigates the use of proof (or acceptance) test data during the reliability based design optimization of structural components. It is assumed that every component will be proof tested and that the component will only enter into service if it passes the proof test. The goal is to reduce the component weight, while maintaining high reliability, by exploiting the proof test results during the design process. The proposed procedure results in the simultaneous design of the structural component and the proof test itself and provides the designer with direct control over the probability of failing the proof test. The procedure is illustrated using two analytical example problems and the results indicate that significant weight savings are possible when exploiting the proof test results during the design process.

Ventor, Gerharad

A Semantic Basis for Proof Queries and Transformations

We extend the query language PrQL, designed for inspecting machine representations of proofs, to also allow transformation of proofs. PrQL natively supports hiproofs which express proof structure using hierarchically nested labelled trees, which we claim is a natural way of taming the complexity of huge proofs. Query-driven transformations enable manipulation of this structure, in particular, to transform proofs produced by interactive theorem provers into forms that assist their understanding, or that could be consumed by other tools. In this paper we motivate and define basic transformation operations, using an abstract denotational semantics of hiproofs and queries. This extends our previous semantics for queries based on syntactic tree representations.We define update operations that add and remove sub-proofs, and manipulate the hierarchy to group and ungroup nodes. We show that

Proof Queries

Optimal periodic proof test based on cost-effective and reliability criteria

An exploratory study for the optimization of periodic proof tests for fatigue-critical structures is presented. The optimal proof load level and the optimal number of periodic proof tests are determined by minimizing the total expected (statistical average) cost, while the constraint on the allowable level of structural reliability is satisfied. The total expected cost consists of the expected cost of proof tests, the expected cost of structures destroyed by proof tests, and the expected cost of structural failure in service. It is demonstrated by numerical examples that significant cost saving and reliability improvement for fatigue-critical structures can be achieved by the application of the optimal periodic proof test. The present study is relevant to the establishment of optimal maintenance procedures for fatigue-critical structures.

Yang, J.-N.

A comparison of single-cycle versus multi-cycle proof testing strategies

Proof testing was a useful supplement to conventional nondestructive evaluation (NDE) of space shuttle main engine (SSME) components. Since many of these components involve thin sections and high toughness materials, such as Inconel 718, conventional single-cycle proof test logic is not applicable due to the propensity for stable crack growth during the proof tests. Experience with five-cycle proof testing of SSME components is summarized and a framework is outlined for understanding multi-cycle proof testing using the fracture mechanics concept of a resistance curve. Extreme value statistics are also used to propose an empirical approach to compare the advantages and disadvantages of single- versus multi-cycle proof testing. The importance of the initial flaw size distribution and specimen thickness in such a comparison is also discussed.

Hudak, Stephen J., Jr.

Evaluation of proof testing as a means of assuring mission success for the Space Shuttle thermal protection system

The reliability analysis of a thermal protection system (TPS) incorporating low density, fibrous ceramic materials must take into account the time-dependency and variability of the system's strength. Fracture mechanics concepts can be used to estimate the allowable strength and expected lifetime, as well as to define a proof test scheme for assuring mission success of TPS. The aim of this study was to evaluate the proof testing scheme used on the TPS of the Space Shuttle with these fracture mechanics concepts. The analysis confirmed that proof testing was necessary for the undensified system and that proof testing should lead to adequate reliability with respect to the design stresses. For the undensified system, fracture mechanics predictions were confirmed by measuring the strength of samples that survived proof testing. It was also found that the time-dependent nature of the system's strength was controlled mainly by the ceramic and that this time-strength dependency is similar to that observed for bulk glasses that have compositions similar to the glass fibers present in the ceramic tiles.

Green, D. J.

Proof test methodology for composites

The special requirements for proof test of composites are identified based on the underlying failure process of composites. Two proof test methods are developed to eliminate the inevitable weak fiber sites without also causing flaw clustering which weakens the post-proof-test composite. Significant reliability enhancement by these proof test methods has been experimentally demonstrated for composite strength and composite life in tension. This basic proof test methodology is relevant to the certification and acceptance of critical composite structures. It can also be applied to the manufacturing process development to achieve zero-reject for very large composite structures.

Wu, Edward M.