DDSim: A hierarchical, probabilistic, multiscale damage and durability simulation system – Part I: Methodology and Level I

Abstract

Current tools for fatigue life prediction of metallic structural components are limited in some or all of the following capabilities: geometry of, and boundary conditions on, the affected structural component, automation of the simulation process, randomness of the primary variables, and physics of the damage evolution processes.

DDSim, a next-generation damage and durability simulator, addresses each of these limitations with a hierarchical, multiscale, “search and simulate” strategy. This hierarchical strategy consists of three levels. Level I, described in this paper, performs an initial, reduced order, conservative screening, based on a linear finite element analysis of the uncracked component, to determine the most life-limiting locations for intrinsic material flaws. Initial flaw size can be specified deterministically, or generated randomly from statistical descriptions of the microstructure and used in Monte Carlo simulation. The result is a scalar field of predicted life over the entire domain of the structure. The benefits of the Level I analysis include a high degree of automation, solution speed, and easy implementation of high performance parallel computing resources. A validation case study of Level I is described.

Levels II and III are outlined herein, but will be described in further detail in subsequent papers. The Level II analysis uses FRANC3D to accurately predict the number of cycles consumed by microstructurally large crack growth processes. Level III performs multiscale analyses to accurately predict the cycles consumed in microstructurally small crack growth processes.

Introduction

Structural reliability is of utmost importance in structural design of space vehicles in extreme environments. Of particular interest to NASAs Project Constellation return-to-the-moon mission are highly reliable thermal protection systems (TPS) and primary airframe structure subjected to thermal gradients. Life and residual strength prediction under high reliability constraints is very difficult due to the lack of adequate models, experimental framework to guide design and manufacturing processes, and numerical simulation tools that accurately predict limit states. To that end, NASAs Constellation University Institutes Project (CUIP) [1] has formed a virtual institute, Structures and Materials for Extreme Environments (SMEE), whose focus is on research and development of tools and methodologies to support Project Constellation’s mission.

Furthermore, the issue of aging aircraft is again receiving increasing attention recently from both our armed forces and the US Federal Aviation Administration. Specifically, the Defense Advanced Research Projects Agency (DARPA) has recognized the need for more reliable structural prognoses and, consequently, is currently funding an entire prognosis program [2]. Current life prediction tools and methods hinder flight/combat readiness due to imprecision and raise cost due to over, or misguided, conservatism. These undesirable effects are caused by models that are not physically grounded and undervalue the inherently random nature of the material systems. The work reported herein addresses the needs identified in these NASA and DARPA projects.

Damage prognosis is the estimate of a structural system’s remaining useful life [3]. There are many contributing elements to successful structural prognosis including quantifying the current status of the structural integrity, recording previous loading history, estimating future loading patterns and developing robust material models that account for such things as environmental effects. A next-generation tool is required to blend all of this useful, and generally random, information to simulate the structure’s remaining life. Durability, on the other hand, is the structure’s resilience to its loading conditions and its ability to maintain serviceability [4]. A durable structure can reduce inspection intervals, thereby reducing the cost of operation. A tool to simulate structural durability must incorporate much of the same input data as a damage prognosis tool and account for damage incubation and nucleation caused by defects within the material system itself.

The traditional damage tolerance approach to fatigue life assessment assumes defects – due to intrinsic material flaws, machining, or assembly processes – exist prior to service [5], [6]. Damage tolerance procedures, by definition, do not account for fatigue life consumed by crack nucleation or crack growth prior to the assumed initial flaw size. This portion of the fatigue life of the vehicle can be substantial. The simplest and fastest damage tolerance assessment uses an approximate geometry and a fatigue analysis code such as NASGRO or AFGROW [7], [8]. Software packages like these have been successfully designed to exploit the simplicity of hand-book stress intensity factor (SIF) solutions for fast calculations, but do so at the expense of fidelity. To a large degree, the accuracy of the predictions is dependent on the judgment of the engineer who must usually simplify geometry and local stress fields.

In the most elaborate procedure, finite element analysis (FEA) includes crack geometry in the structural model and allows the crack to evolve based on the stress field local to the crack front. The fields computed by the FEA are used in conjunction with a fracture mechanics code such as FRANC3D [9] to calculate the SIF history. The analyst must manually enter the computed SIF history into the fatigue analysis code to apply the fatigue crack growth model. If any probabilistic analysis is conducted, a third code, such as NESSUS [10], may be employed. NESSUS is a probabilistic driver that can be used in the damage tolerance assessment given information about random inputs. In the case of aircraft turbine rotor disks, a probabilistic life prediction code such as DARWIN [11] might be used in place the fatigue analysis code to perform probabilistic analysis.

The procedures of the current state-of-practice have been developed to take full advantage of currently available or readily measurable material data and, hence, use empirical crack growth rate models instead of models which simulate the physics of crack growth. The result is a practical and useful, yet limited, set of tools for fatigue life prediction. The least accurate procedure is fast, but does not account for the arbitrary stress fields that can be present in complex geometry. The most accurate procedure is a time-consuming, multi-step, and multi-code effort.

In summary, the current technology of life prediction and damage tolerance tools exhibit some or all of the following deficiencies:

• Restricted physics – empirical crack growth laws; no multi-scale analysis; and averaged damage effects.

• Restricted flaw geometry – hand-book solutions; and absence of natural crack growth.

• Low automation – multiple codes requiring significant human intervention.

• No or little stochastics – increased automation, unrestricted geometry and better physics would allow for the inherent stochastics of the problem to be incorporated.

Clearly, there is high demand for a prognosis methodology that extends beyond current damage tolerance practice. An automated prognosis tool that embraces the physics and recognizes the probabilistic nature of the problem is highly desirable. To that end, this paper outlines a next generation Damage and Durability Simulator, DDSim, that has been developed using a hierarchical “search and simulate” strategy. Also presented is detailed information about implementation and validation of the first level of the hierarchy. DDSim Level I searches the domain of a structure using life prediction estimates based on current best-practice methods to choose sub-domains where the higher levels simulate the multiscale fatigue process with greater fidelity. The methodology presented herein is general enough to be extended to other material systems; however, the focus of this discussion will be on the aerospace-grade aluminum alloy 7075-T651.

The data demands for the next-generation methodology will require extensive materials databases, as will become evident in the subsequent section, and the computational demands will be extensive. However, experimental capabilities, data storage techniques and information sharing tools are undergoing commensurate technological advances. This methodology is driven by the notion that development of new tools should not be restricted by currently available technologies. Rather, new tools should be developed with an eye toward what will become available in the not-so-distant future.

The remainder of this paper is organized as follows: a description of the multiscale and stochastic nature of the fatigue damage in 7075-T651; an outline for DDSim, a new, three-tiered, methodology in damage and durability simulation; background for the Level I tool, the first of the three hierarchical tiers; implementation of the Level I tool; a validation case study of Level I; and conclusions.