{"id":229,"date":"2025-09-23T11:28:11","date_gmt":"2025-09-23T17:28:11","guid":{"rendered":"https:\/\/thesinewave.com\/home\/?page_id=229"},"modified":"2025-09-23T12:28:02","modified_gmt":"2025-09-23T18:28:02","slug":"insights","status":"publish","type":"page","link":"https:\/\/thesinewave.com\/home\/insights\/","title":{"rendered":"Insights"},"content":{"rendered":"\n

Part One: Fracture Mechanics Flaw Evaluation<\/strong><\/h1>\n\n\n\n

Linear Interpolation<\/strong><\/h1>\n\n\n\n

The frustration with interpolation. What to do when the aspect ratio isn\u2019t on the table?<\/p>\n\n\n\n

Guru, expert, wizard, savant\u2026 Please do not hurl insults at me. My involvement with Fracture Mechanics (FM) started pretty much like anybody else \u2013 by being pulled through a knot-hole sideways and making mistakes. These posts are just some of the things learned over the years and hopefully will help people out with some of the more common questions.<\/p>\n\n\n\n

Understanding that the ASME tables are a canned solution for flaw acceptance criteria (yes, some flaws are acceptable). Also, the individual tables are specific to each Code book that uses them. Sec. VIII, Sec. XI, and B31.3, being the most common that we UT people encounter. That said, here we go.<\/p>\n\n\n\n

To use these tables, we draw a rectangular box, with the length parallel and the height normal to the inside surface, around the flaw\u2019s extremities, then get a flaw height (hf<\/sub>)<\/em> to length (lf<\/sub>)<\/em> ratio and call it an aspect ratio (hf<\/sub>\/lf<\/sub>) (this is B31 nomenclature, it would be a\/l in Sec. VIII and XI).<\/em> Pretty simple right? So far, so good until you realize you have some weirdo number that doesn\u2019t fit neatly in the table. What to do? (hint \u2013 read the notes, always read the notes!)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Can I just split the difference? No, please don\u2019t do this. This would be averaging and not linear interpolation.<\/p>\n\n\n\n

Can I round the numbers? Yes, but only DOWN to the lower (more conservative) number in the column.<\/p>\n\n\n\n

In this case 0.33 would become 0.30. Always round to the lower number, and never up (e.g., 0.34, being closer to 0.35, would still round down to 0.30).<\/p>\n\n\n\n

The problem with just rounding (other than being lazy \u2013 after all, you went through a lot of effort to get your best numbers. Why stop now?) is that you could unfairly penalize the component. Repairs are bad for everyone and the component. Leaving a benign flaw alone is far better than needlessly grabbing an arc gouger or grinder and re-welding a localized area.<\/p>\n\n\n\n

The other (most correct) option available is to use linear interpolation. What is interpolation? Interpolation is a method of creating a new data point based on a set of known data points. This allows us to create those sections of the table that are not included in it. (they\u2019re in there, they just don\u2019t know it yet.)<\/p>\n\n\n\n

Locate the two aspect ratios that your \u201cactual\u201d aspect ratio value fits between. You will be using the immediate value(s) above and below your actual number. In this example 0.33 fits between 0.30 and 0.35 on the table (in the equation below, these will be our X1<\/sub> and X2<\/sub> values respectively).<\/p>\n\n\n\n

Next, follow the rows across to obtain the two corresponding numbers from the Hf\/Tw column. As you can see, we will land somewhere between 0.064 and 0.074 (for this equation these known values will be our Y1<\/sub> and Y2<\/sub> values).<\/p>\n\n\n\n

Here is a common formula to accomplish interpolation. There are tons of videos and detailed info on the web. If you get a spreadsheet from your buddy, make sure you test drive it before use.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

(Note: you can interpolate in any direction, it also works going across to get the correct T value. See note \u201c(b)\u201d below the table.)<\/p>\n\n\n\n

An easy way to think about interpolation is to represent it in a simple X, Y graph as shown below. In this case \u201cX\u201d represents the aspect ratio, and \u201cY\u201d represents the acceptance criteria values. It could also be the other way around, its user defined.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

In the next post\u2026 Can you have an aspect ratio greater than 0.50? (hint \u2013 the answer is in the \u201cno\u201d.)<\/p>\n\n\n\n

Part Two: Fracture Mechanics Flaw Characterization<\/strong><\/h1>\n\n\n\n

What is \u201c2a\u201d?<\/strong><\/h1>\n\n\n\n

First off, what we do as UT practitioners is flaw characterization and not Fracture Mechanics. \u201cFracture Mechanics is the science of determining the resistance to fracture of a material or engineering component\u201d (EPRI Primer NP-5792-SR, 1991).<\/p>\n\n\n\n

About 3-4 times a year someone will call asking a question about running the fracture mechanics formulas in the ASME Code sections.<\/p>\n\n\n\n

First things first, ensure you are looking at the right tables, B31, Section VIII, and Section XI are all different. It makes sense as these are all different products from piping, pressure vessels, and Nuclear Inservice.<\/p>\n\n\n\n

Probably the #1 question is what to do with \u201c2a\u201d for subsurface flaws and this generally stems from this figure in Section VIII.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The calculation to apply the accept \/ reject tables is \u201ca\/l\u201d for your aspect ratio. The confusion comes from not realizing that the flaw height in this figure is \u201c2a\u201d, and not just \u201ca\u201d. Therefore the magic number you use in the \u201ca\/l\u201d calculation is HALF the actual flaw height. <\/strong>Otherwise the calculation at the top of the table would read \u201c2a\/l\u201d, which it does not. Some have even asked if you are supposed to double the flaw height, no you do not.<\/p>\n\n\n\n

Why is this? \u2013 Great question and to be honest it could be spelled out better in the books. The reason is, a subsurface flaw has two directions to exert force, essentially towards the I.D. and the O.D. therefore, in the tables only half is considered.<\/p>\n\n\n\n

Remember though all the Code Books are different. Do not mix and match.<\/p>\n\n\n\n

Here is a similar drawing from Annex R of B31.3:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The nomenclature of drawing is different, what was \u201c2a\u201d<\/em> suddenly became \u201chf\u201d,<\/em> \u201cl\u201d<\/em> is now \u201clf\u201d,<\/em> and the same for \u201cS\u201d <\/em>becoming \u201cSf\u201d.<\/em> Most importantly is the omission of the \u201c2\u201d.<\/em> In the case of the B31.3 code, you use the ENTIRE flaw height<\/strong> for the calculations.<\/p>\n\n\n\n

What? Why is this different? If you notice the values in the tables from Sec. VIII and B31.3 are different. The B31 tables have already built in compensation for the full flaw height.<\/p>\n\n\n\n

So please remember the different book sections are all for different products and are not interchangeable. Take your time, ask questions, you\u2019ll be fine, and always, always read the notes under the Tables!<\/p>\n\n\n\n

Part 3: Fracture Mechanics Flaw Evaluation<\/strong><\/h1>\n\n\n\n

A Flaw That Exceeds 0.50 Aspect Ratio<\/strong><\/h1>\n\n\n\n

If you look at the ASME acceptance tables in Sec VIII, Sec XI, and B31.3 you realize that all tables only go up to an aspect ratio (a\/l<\/em>) of 0.5. The exception being the subsurface table of B31.3, which goes up to 1.0. You\u2019ll also remember the B31 Code uses the entire flaw height for the aspect ratio, and the others use half (or \u201c2a\u201d rather).<\/p>\n\n\n\n

Reading through the paragraphs of Sec VIII or XI, they will explicitly tell you that you cannot have an aspect ratio (a\/l<\/em>) greater than 0.5, whereas the B31 Code does not address it. Why is this, and what do I do with this flaw?<\/p>\n\n\n\n

Not sure the real reason why, but I can tell you that B31.3 Annex R was adopted in the mid 20-teens and was written by NDE people for NDE people. Whereas the tables in the other Code sections are much older.<\/p>\n\n\n\n

So, can you have an aspect ratio that exceeds 0.50? \u2013 yes in real life you absolutely can. They are not very common, but it is possible. Imaging a stack of individual flaws that make the proximity rules and are therefore counted as a single flaw. Probably the most likely situation, but again not very common.<\/p>\n\n\n\n

Still, why does the Code say you can\u2019t have one? Well, it doesn\u2019t. Not really anyways, what it is really telling you is that you cannot apply it to the tables\u2026 In the shape it\u2019s in. The Code doesn\u2019t directly tell you what to do with it, at least not in a sentence.<\/p>\n\n\n\n

This was one of the worst Easter egg hunts I had ever been on with these books and may warrant a little criticism. However, I did find it in the figures (pics). Not very obvious, and I can\u2019t help but feel that a simple sentence would suffice stating that: \u201cA flaw having an aspect ratio exceeding a\/l<\/em> = 0.5 shall be extended in the l<\/em> dimension such that l<\/em> = 2a\u201d Bam, done\u2026 Maybe I\u2019ll ask?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

So yes, in the case of having a flaw with a greater than 0.50 aspect ratio the answer is to artificially extend the length of your flaw to the 2a dimension. Thus, giving it an aspect ratio of 0.5.<\/p>\n","protected":false},"excerpt":{"rendered":"

Part One: Fracture Mechanics Flaw Evaluation Linear Interpolation The frustration with interpolation. What to do when the aspect ratio isn\u2019t on the table? Guru, expert, wizard, savant\u2026 Please do not hurl insults at me. My involvement with Fracture Mechanics (FM) started pretty much like anybody else \u2013 by being pulled through a knot-hole sideways and … <\/p>\n

Continue reading “Insights”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-229","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/pages\/229","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/comments?post=229"}],"version-history":[{"count":7,"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/pages\/229\/revisions"}],"predecessor-version":[{"id":257,"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/pages\/229\/revisions\/257"}],"wp:attachment":[{"href":"https:\/\/thesinewave.com\/home\/wp-json\/wp\/v2\/media?parent=229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}