# Superimpose DELs weighted on different lifetime

Hi everybody,

I have got a likely pretty straightforward question.

Let assume that I have a DEL value weighted over 20 years and a second value weighted over 0.25 years: is it possible to get a overall DEL weighted over a 20.25 years lifetime, starting from the two above? Nref = 1E+08 cycles and Woehler slope m=4.

I would expect the solving formula to look like:

DEL(20.25) = (((DEL(20)^m20 + DEL(0.25)^m0.25)*Nref/(20.25))^(1/m))/Nref

Am I on the right track or not? Please shed a light.

I thank you all in advance.

Dear Francesco,

The damage-equivalent load (DEL) is defined as follows:

DEL = ( SUM( n_k*L_k^m, k = 1, 2, …, N )/n_eq )^(1/m)

where,
N = number of load-range bins
n_k = number of cycle counts in the k’th load-range bin
n_eq = number of equivalent cycle counts
m = Whoeler material exponent

I’m not exactly sure how you are defining Nref. I’m assuming you mean that Nref is the number of equivalent cycle counts per year, such that 20*Nref is the number of equivalent cycle counts in 20 years.

I’m also not clear on how you are defining DEL(20) and DEL(0.25). If you mean that DEL(20) is a DEL based on Nref that acts for 20 years out of a 20.25-year period and DEL(0.25) is a DEL based on Nref that acts for 0.25 years out of a 20.25-year period, and my assumption about Nref is correct, than DEL(20.25) is:

DEL(20.25) = ( ( 20NrefDEL(20)^m + 0.25NrefDEL(0.25)^m )/( 20.25*Nref ) )^(1/m)

Notice that Nref cancels out, leaving:

DEL(20.25) = ( ( 20DEL(20)^m + 0.25DEL(0.25)^m )/( 20.25 ) )^(1/m)

However, there could be other interprations of Nref, DEL(20), and DEL(0.25). If my interprations are not correct, please clarify.

Best regards,

Dear Jason,

your thoughts about Nref, DEL(20) and DEL(20.25) are absolutely right. Indeed, I myself came up with the same formula you wrote down 10’ after posting my question.

I just wanted to have my idea supported by somebody who has a more consistent knowledge than me.

I really thank you in advance.

Kindest regards from Germany.