# US 10,309,883 B2 · Analyzing structural durability in the frequency domain > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,309,883 B2 - Document ID: US10309883B2 - Status: Granted - Kind: B2 - Application number: 14/554,486 - Filed: 2014-11-26 - Published: 2015-04-23 - Granted: 2019-06-04 - Earliest claimed: 2007-11-30 - Assignees: The Boeing Company - Applicants: The Boeing Company - Inventors: Mostafa Rassaian; Jonathan H. Gosse; Stephen Christensen - Web page: https://patentgrep.com/patent/US10309883B2 ## CPC - G01N 3/32: by applying repeated or pulsating forces - G01N 29/045: {by imparting shocks to the workpiece and detecting the vibrations or the acoustic waves caused by the shocks (measuring resonant frequency G01H13/00; measuring strength properties by application of mechanical stress G01N3/00)} - G01N 29/12: by measuring frequency or resonance of acoustic waves {(measuring frequency or resonant frequency of mechanical vibrations or acoustic waves in general G01H1/06, G01H3/04, G01H13/00; acoustic resonators G10K11/04; vibration or shock testing of structures G01M7/00)} - G06F 30/15: Vehicle, aircraft or watercraft design - G06F 30/17: Mechanical parametric or variational design - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM] - B29C 66/721: {Fibre-reinforced materials (B29C66/729 takes precedence)} - B29C 66/7212: {characterised by the composition of the fibres} - B64C 2001/0072: {from composite materials} - G01N 2291/02827: Elastic parameters, strength or force - G06F 2113/26: Composites - Y02T 50/40: Weight reduction - G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - B29C: SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING (making preforms B29B11/00; making laminated products by combining previously unconnected layers which become one product whose layers will remain together B32B37/00 - B32B41/00) - B64C: AEROPLANES; HELICOPTERS - Y02T: CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION ## Abstract A method of analyzing the durability of a structure. Load-controlled testing is performed on samples of a composite material of the structure to relate critical strain invariants of the material to cyclic rates of strain invariant accumulation and frequencies associated with the cyclic rates. The material is characterized based on effective properties of the material, including the cyclic rates of strain invariant accumulation. Laminate properties and a geometrical definition of the structure are used to obtain a parametric model. Material characterizations are used to determine model element frequency responses to applied load conditions. Each element's frequency responses and critical strain invariants are used to determine whether damage is indicated at the element. Progression of damage is tracked and accounted for in the model. ## Claims ### Claim 1 A method of analyzing durability of a composite structure, comprising: performing load-controlled testing of samples of a plurality of materials to be used as part of a structure, the plurality of materials comprising at least one composite material, wherein the load-controlled testing includes determining at least one effective material property of the at least one composite material based on an accumulative invariant approach; forming a parametric model of the structure based on the load-controlled testing of the samples and a geometric definition of the structure, wherein the parametric model includes a plurality of elements based on the geometric definition of the structure, and the at least one effective material property of the at least one composite material; and determining, using the parametric model, failure characteristics of the structure under load conditions by determining frequency responses of the plurality of elements to data of the load conditions applied to the plurality of elements in the parametric model, wherein the at least one effective material property is based on interactions of a plurality of phases of the at least one composite material, the phases including a polymeric matrix phase and a fiber reinforcement phase, and wherein determining the failure characteristics of the structure further comprises assessing failure within the fiber reinforcement phase of the at least one composite material and determining a percentage of plies that have failed. ### Claim 2 (depends on 1) The method of claim 1, wherein the determining the at least one effective material property includes determining at least one of: a first relationship between critical strain invariants of the materials versus cyclic rates of strain invariant accumulation, and a second relationship of load frequencies applied to the materials versus cyclic rates. ### Claim 3 (depends on 2) The method of claim 2, wherein the critical strain invariants of the materials are based on at least one of: temperature, loading rate, and moisture content. ### Claim 4 (depends on 2) The method of claim 2, wherein the first relationship is based on applying a load to samples of the materials until predefined critical invariant values are achieved and wherein the cyclic rates are based on applied frequency of the load and a ratio of minimum stress to maximum stress under the load. ### Claim 5 (depends on 1) The method of claim 1, further including determining whether damage would occur at one or more particular location within the structure. ### Claim 6 (depends on 1) The method of claim 1, wherein the performing the load-controlled testing includes performing simple uni-axial tension tests for each of three lamina configurations for each of the materials. ### Claim 7 (depends on 1) The method of claim 1, wherein the determining the frequency responses involves utilizing load conditions having at least one of: static pressure, thermal loads, pre-loads, vibratory loads, shock loads, and acoustic loads. ### Claim 8 (depends on 1) The method of claim 1, further comprising simulating a progression of damage in the materials of the structure when the data of the load conditions are applied. ### Claim 9 (depends on 2) The method of claim 2, wherein the cyclic rates are based on load frequency applied to the materials and input spectrum. ### Claim 10 (depends on 1) The method of claim 1, further comprising conducting parametric studies, using the model parametric model, to identify combinations of materials and structure geometries associated with failure characteristics within predetermined specifications. ### Claim 11 (depends on 1) The method of claim 1, wherein the determining the frequency responses includes displaying, with a user interface, the failure characteristics of the structure in the format of at least one of: a fringe plot and a contour plot. ### Claim 12 (depends on 1) The method of claim 1, wherein the determining the failure characteristics includes performing a response frequency analysis, wherein the response frequency analysis includes at least one of: modal acceleration and modal superposition. ### Claim 13 (depends on 1) The method of claim 1, wherein load-controlled testing of samples involves a limited number of samples such that studies of composite structures can be performed without generating a large number of test samples since the parametric model is used for determining whether damage is indicated to the plies. ### Claim 14 A system for analyzing the durability of a structure, the system comprising at least one processor and memory configured to: receive at least one effective material property of a plurality of materials from load-controlled testing of samples of the plurality of materials to be used as part of a structure, the plurality of materials comprising at least one composite material, wherein the load-controlled testing includes determining the at least one effective material property of the at least one composite material based on an accumulative invariant approach; form a parametric model of the structure based on the load-controlled testing of the samples and a geometric definition of the structure, wherein the parametric model includes a plurality of elements based on the geometric definition of the structure, and the at least one effective material property of the at least one composite material; and determine, using the parametric model, failure characteristics of the structure under load conditions by determining frequency responses of the plurality of elements to data of the load conditions applied to the plurality of elements in the parametric model, wherein the at least one effective material property is based on interactions of a plurality of phases of the at least one composite material, the phases including a polymeric matrix phase and a fiber reinforcement phase, and wherein determining the failure characteristics of the structure further comprises assessing failure within the fiber reinforcement phase of the at least one composite material and determining a percentage of plies that have failed. ### Claim 15 (depends on 14) The system of claim 14, wherein the determining the at least one effective material property includes determining at least one of: a first relationship between critical strain invariants of the materials versus cyclic rates of strain invariant accumulation, and a second relationship of load frequencies applied to the materials versus cyclic rates. ### Claim 16 (depends on 15) The system of claim 15, wherein the critical strain invariants of the materials are based on at least one of: temperature, loading rate, and moisture content. ### Claim 17 (depends on 14) The method of claim 14, wherein the at least one processor and memory are further configured to simulate a progression of damage in the materials of the structure when the data of the load conditions are applied. ### Claim 18 (depends on 14) The system of claim 14, wherein load-controlled testing of samples involves a limited number of samples such that the system can perform studies of composite structures can be performed without generating a large number of test samples since the parametric model is used for determining whether damage is indicated to the plies. ### Claim 19 A non-transitory medium containing processor-readable instructions when performed by a processor cause the processor to perform operations of: receiving at least one effective material property of a plurality of materials from load-controlled testing of samples of the plurality of materials to be used as part of a structure, the plurality of materials comprising at least one composite material, wherein the load-controlled testing includes determining the at least one effective material property of the at least one composite material based on an accumulative invariant approach; forming a parametric model of the structure based on the load-controlled testing of the samples and a geometric definition of the structure, wherein the parametric model includes a plurality of elements based on the geometric definition of the structure, and the at least one effective material property of the at least one composite material; and determining, using the parametric model, failure characteristics of the structure under load conditions by determining frequency responses of the plurality of elements to data of the load conditions applied to the plurality of elements in the parametric model, wherein the at least one effective material property is based on interactions of a plurality of phases of the at least one composite material, the phases including a polymeric matrix phase and a fiber reinforcement phase, and wherein determining the failure characteristics of the structure further comprises assessing failure within the fiber reinforcement phase of the at least one composite material and determining a percentage of plies that have failed. ### Claim 20 (depends on 19) The non-transitory medium of claim 19, further including processor-readable instructions when performed by a processor cause the processor to simulate a progression of damage in the materials of the structure when the data of the load conditions are applied. ### Claim 21 (depends on 19) The non-transitory medium of claim 19, further including processor-readable instructions when performed by a processor cause the processor to conduct parametric studies, using the model parametric model, to identify combinations of materials and structure geometries associated with failure characteristics within predetermined specifications.