Computational method for load enhancement factors and apparatus for executing same

• US 20080154520A1
• Filed: 12/22/2006
• Published: 06/26/2008
• Est. Priority Date: 12/22/2006
• Status: Active Grant

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Taam, Winson, Giancaspro, James W.
• Granted Patent: US 7,877,229 B2
• Time in Patent Office: Days
• US Class Current: 702/34
• CPC Class Codes: B29C 70/00 Shaping composites, i.e. plastics material comprising reinforcements, fillers or preformed parts, e.g. inserts
• CPC Class Codes: G01N 2033/0003 Composite materials

Abstract

A method and computer system for executing a program for calculating Load Enhancement Factor that includes the steps of obtaining coupon test data and storing the coupon test data on an information storage device. Analyzing the coupon test data for fit with a Weibull distribution and other analysis criteria and performing either a Modified Joint Weibull analysis or a Weibull Regression analysis or both a Modified Joint Weibull analysis and a Weibull Regression analysis with an accommodation in the analysis for scatter within the coupon testing data.

Claims

1. A method of calculating a Load Enhancement Factor using Modified Joint Weibull Analysis, comprising the method steps of:

retrieving a data set from an at least one database;

analyzing the data retrieved for fit with a statistical distribution model;

analyzing the data retrieved for statistical conditions;

calculating a stress to life cycle relationship accounting for scatter in the test data; and

calculating a Load Enhancement Factor based on the stress to life cycle relationship.

2. A method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis, comprising the method steps of:

retrieving a test data set from an at least one database;

analyzing the data retrieved for fit with a Weibull distribution model for the data;

analyzing the test data set retrieved to determine if at least two coupons have been tested and if both the applied loads and duration of testing at the component-level were varied;

computing an at least one shape parameter for the Weibull distribution model and storing the at least one shape parameter;

computing an at least one scale parameter for the Weibull distribution of the data and storing the at least one scale parameter;

computing a stress to life cycle relationship accounting for scatter in the data through the Weibull distribution data; and

computing the at least one of a Life Factor, a Load Factor and a Load Enhancement Factor based on the stress to life cycle relationship from the computed stress to life cycle relationship, thereby accounting for scatter in the at least one Life Factor, a Load Factor and a Load Enhancement Factor.

3. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 2, wherein the method step of computing an at least one shape parameter further comprises computing the Weibull shape parameter value for fatigue life, (β

_L), using the equation

4. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 3, wherein the method step of computing an at least one shape parameter further comprises computing the Weibull shape parameter value for residual strength, (β

_r) using the equation

5. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 4, wherein the method step of computing an at least one shape parameter further comprises computing the Weibull shape parameter value for static strength, (β

_s), is computed in equation

6. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 5, wherein the method step of computing an at least one shape parameter further comprises solving for the Weibull shape parameter for static strength, Weibull shape parameter for residual strength, and Weibull shape parameter for fatigue life values for the equations using an iterative approach.

7. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Joint Weibull Analysis of claim 6, wherein the method step of computing an at least one scale parameter further comprises calculating the Weibull life scale parameter for each stress level using equation

8. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 7, wherein the method step of computing an at least one scale parameter further comprises calculating the Weibull scale parameter for residual strength using equation

9. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 8, wherein the method step of computing an at least one scale parameter further comprises calculating scale parameter for static strength using equation

10. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 2, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises obtaining values for Chi-squared distribution and Gamma functions.

11. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 8, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises the method step of obtaining user input for a desired confidence level (γ

), calculating the value of the Chi-squared distribution for the obtained level of confidence (χ

<sub>γ

,2nL</sub>) wherein 2n_L are the degrees of freedom corresponding to coupon-level test data.

12. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 11, wherein the method step of obtaining values for the Chi-squared distribution and Gamma functions further comprises calculating values of the Gamma function for the life shape parameter using the equation:

13. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 12, wherein the method step of obtaining values for the Chi-squared distribution and Gamma functions further comprises calculating the values of the Gamma function for the residual strength shape parameters using the equation:

14. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 11, wherein the method step of obtaining values for the Chi-squared distribution and Gamma functions further comprises storing values for the Gamma function for varying shape parameters in a database.

15. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 10, wherein the method step of obtaining values for the Chi-squared distribution and Gamma functions further comprises a lookup step, wherein the value of the chi square and gamma functions are determined by the lookup step in a table of stored values in the database.

16. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 14, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises, calculating mean static strength using the equation:

17. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 16, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises calculating mean residual strength using the equation:

18. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 17, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises calculating mean fatigue life using equation:

19. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 18, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises obtaining a reliability rating and calculating the design life at a desired reliability and the residual strength allowable at the reliability computed using the equations:

20. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 19, wherein the method step of computing a stress to life cycle relationship accounting for scatter further comprises calculating static strength allowable at the reliability using the equation:

21. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 20, wherein the method step of computing at least one of a Life Factor, a Load Factor and a Load Enhancement Factor further comprises the method step of computing the Life Factor using the equation:

22. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 21, wherein the method step of computing at least one of a Life Factor, a Load Factor and a Load Enhancement Factor further comprises the method step of computing the Load Factor, (S_F) using the equation:

23. The method of computing at least one of a Load Factor, a Life Factor and a Load Enhancement Factor using Modified Joint Weibull Analysis of claim 22, wherein the method step of computing at least one of a Life Factor, a Load Factor and a Load Enhancement Factor further comprises the method step of computing Load Enhancement Factor using the equation:

24. A method of calculating a Load Enhancement Factor using Weibull Regression Analysis, comprising the method steps of:

obtaining coupon test data;

applying a Weibull distribution regression function to the coupon test data to develop an estimated stress to fatigue life curve and applying an equation to relate the log of a scale parameter of the Weibull distribution regression function with the log of a stress level of the stress to fatigue life curve;

implementing an estimation procedure to incorporate the stress to fatigue life relationship in the computation of the Load Enhancement Factor through the intercept and slope of the estimates of the stress to fatigue life curve ({circumflex over (θ

)}₀,{circumflex over (θ

)}₁); and

obtaining a confidence level and using a variance and a co-variance matrix developed from the estimation procedure to compute the Load Enhancement Factor.

25. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 24, wherein the coupon test data is from a single stress level.

26. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 24, wherein the coupon test data is from multiple stress levels and includes static strength data.

27. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 24, wherein the Weibull distribution function is defined by the equation:

28. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 27, wherein the equation to relate the log of a scale parameter of the Weibull distribution function with the log of a stress level of the stress to fatigue life curve is a linear relationship between a log of the scale parameter and a log of stress level that is established through the equation:

ln(α

₁)=θ

₀+θ

₁ln(S_i)

, wherein α

_i is the scale parameter for the i^th group, θ

₀ represents the intercept parameter of the Weibull regression model, θ

₁ represents the slope parameter of the Weibull regression model, and S represents the stress level applied in fatigue test or static strength for the i^th group.

29. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 28, wherein the method step of implementing an estimation procedure further comprises implementing an estimation procedure with y_ij=ln(x_ij), and where the probability density function and the cumulative distributions for y are computed by equations:

30. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 29, wherein the method step of implementing an estimation procedure further comprises computing a variance and a covariance estimate for θ

₀, θ

₁, and σ

from the inverse of an observed information matrix, {circumflex over (Σ

)}=I₀<sup>−

1</sup>, provided by the equation;

31. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 30, wherein the method step of establishing a confidence level further comprises establishing an A-basis value of a 95% lower confidence limit for the 100q^th percentile, Y_q(S), using equation:

Ŷ

_q(S)−

1.645√

{square root over (V(Ŷ

_q(S))}),

wherein the 100 q^th percentile estimate at S is Ŷ

_q(S)={circumflex over (θ

)}₀+{circumflex over (θ

)}₁ln(S)+C_q{circumflex over (σ

)}, and its variance is approximated by the expression;

V(Ŷ

_q(S))=V({circumflex over (θ

)}₀)+ln(S)²V({circumflex over (θ

)}₁)+C_q²V({circumflex over (σ

)})+2ln(S)Cov({circumflex over (θ

)}₀, {circumflex over (θ

)}₁)+2C_qCov({circumflex over (θ

)}₀,{circumflex over (σ

)})+2ln(S)C_qCov({circumflex over (θ

)}₁, {circumflex over (σ

)}),

wherein C_q=ln(−

ln(1−

q)).

32. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 30, wherein the method step of establishing a confidence level further comprises establishing a B-basis value as a 95% lower confidence limit expressed as equation:

Ŷ

_q(S)−

1.645√

{square root over (V(Ŷ

_q(S))}).

33. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 30, further comprising the method step of obtaining user input for duration of one lifetime.

34. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 30, wherein the method step of computing the Load Enhancement Factor further comprises evaluating Load Enhancement Factor at N₀ lifetime is defined through the equation:

35. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 34, wherein the method step of computing the Load Enhancement Factor further comprises solving for S_E through the equation:

36. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 35, wherein the method step of computing the Load Enhancement Factor further comprises solving for S_B through the equation:

X₁=exp[{circumflex over (θ

)}₀+{circumflex over (θ

)}₁ln(S_B)]exp[C_0.10{circumflex over (σ

)}−

1.645√

{square root over (V(Ŷ

_0.10|S_B))}]

and using a nonlinear solver on the equation.

37. The method of calculating a Load Enhancement Factor using Weibull Regression Analysis of claim 36, wherein the computation of the Load Enhancement Factor includes calculating a Life factor described in equation:

38. A method of certifying an aircraft that includes a composite component, the method comprising:

calculating a Load Enhancement Factor using Modified Joint Weibull Analysis, wherein calculating the Load Enhancement Factor comprises the steps of;

retrieving a data set from an at least one database;

analyzing the data retrieved for fit with a statistical distribution model;

analyzing the data retrieved for statistical conditions;

calculating a stress to life cycle relationship accounting for scatter in the test data; and

calculating a Load Enhancement Factor based on the stress to life cycle relationship.

39. A method of evaluating a composite component of an aircraft, the method comprising:

calculating a Load Enhancement Factor using Modified Joint Weibull Analysis, wherein calculating the Load Enhancement Factor comprises the steps of;

retrieving a data set from an at least one database;

analyzing the data retrieved for fit with a statistical distribution model;

analyzing the data retrieved for statistical conditions;

calculating a stress to life cycle relationship accounting for scatter in the test data; and

calculating a Load Enhancement Factor based on the stress to life cycle relationship.

40. A computer system operating a computer program for calculating a Load Enhancement Factor, comprising:

obtaining coupon test data;

storing said coupon test data on an information storage device;

a program segment analyzing said coupon test data for fit to a Weibull distribution, the program ending in response to the coupon test data not fitting a Weibull distribution;

a program segment analyzing said coupon test data to determine if a single stress level was tested in the coupon test data;

a program segment determining if sufficient runout data is available if the step for analyzing the coupon test data for a single stress level is positive, and if the step of determining sufficient runout is available is negative, ending the program;

determining if sufficient static strength data is available in the coupon test data if the method step of determining if sufficient runout data is affirmative, and if the step of determining if sufficient static strength data is available is negative executing a Modified Joint Weibull Analysis code segment;

executing at least one of a Modified Joint Weibull Analysis code segment and a Weibull Regression code segment with static strength if the method step of determining if sufficient static strength data is affirmative;

determining if a single replicate is available/was tested if the step for analyzing the coupon test data for a single stress level is negative, and if a determination is made that a single replicate was tested executing a Weibull regression code segment;

a program segment determining if sufficient runout data is available if the step of determining if a single replicate is available/was tested is negative, and if a determination is made that sufficient runout is not available, ending the computer program; and

determining if sufficient static strength data is available if the method step of determining if sufficient runout data is available is affirmative, and if the step of determining if sufficient static strength data is available is positive, executing at least one of a Modified Joint Weibull code segment and an at least one Weibull Regression Analysis code segment with static strength computations to compute an LEF and if the step of determining if sufficient static strength data is available is negative, executing at least one of a Modified Joint Weibull code segment and an at least one Weibull Regression Analysis code segment without static strength computations.