toddler;

I'll be the first one to admit I am not a Metallurgist but will make some comments to your posting:

1. From a cross section of a groove or fillet weld, what is the width of the HAZ? 
(jon20013: In my opinion, this question should be a little more specific, there are many variables which could affect the width of the HAZ).

2. Is the width of the HAZ uniform through out the thickness? 
(jon20013: Again, I believe there are too many variables without knowing some specific details).

3. On matters of hardness testing, where do we expect to fail, near the root? middle, or near the top? Why? 
(jon20013: same as above, which processes, material thickness, alloys, parameters?).

4. Normally, hardness is taken from weld/HAZ R-L/basemetal across a line drawn midway and 2mm from top and bottom. What code provides details of this test/location? Is the hardness values from B31.3, table 331.1.1 applies to PQRs?
(jon20013: In our case, we use NACE MR0175/ISO 15156 but this is likely a project specific application).

I think your questions will stimulate some good responses.  It may be that my comments above simply highlight my lack of expertise in the metallurgy field, please let me know?  I'm interested in reading responses from js55 and others who clearly have a better expertise in metallurgy than myself.

As for codes the following would be a good start in answering some of your questions.

1. Width of the haz will vary depending on process, heat etc.
2. As for uniform haz, a machine weld will be close, but it's going to depend on what you are calling uniform.
3. If it's failing the hardness test, theres a process/metallurgy or operation failure to follow the proper process. It can fail at any of the points you listed.
4:
part A of 4
ASTM E 18 Test Methods for Rockwell Hardness and Rockwell
Superficial Hardness of Metallic Materials

ASTM A 370  Standard Test Methods and Definitions for
Mechanical Testing of Steel Products

part B of 4
The hardness values never make it to the essential variables as found in section IX etc. If a referencing code gives a specific limit, that limit takes precedence, and therefore it will apply to the pqr not because it's an essential variable in Section IX, but because it is a requirement of the referencing code.
A quote from 04 Section IX QW 100 general:

" Other sections of the code may specify different requirements than those specified by this section. Such requirements take precedence over those of this section, and the manufacture or contractor shall comply with them".

Part C of 4
One reason that jumps to mind is an increase in hardness is a decrease in toughness. Even though you past the impact, a localized area of hardness could slip by, and later act as a stress notch. Thats just the one that jumps into my mind, there are several reasons, but at the end of the day, it's a moot point when it's specified by code or contract docs.

Anyway, thats my take on it for what it's worth,
Gerald

Toddler, I think you need to understand a few basic things and I would like to try and help explain. 

1. "How wide is the HAZ?" Think what HAZ stands for, heat affected zone. This means any area of the base material which will have it's mechanical or corrosion resistant properties altered by the heat generated by welding. Different materials do not behave in the same way when welding so you cannot make a general statement as to how wide it will be.

2. Generally speaking if the same process/parameters are used the HAZ would be expected to be fairly uniform.

3. Again a general statement cannot be made. For carbon steels the highest hardness could be expected under the toe of the last capping run, for low alloyed steel on the weld metal. For super duplex the weld root can fail due to work-hardening caused by welding stresses.

4. American codes I believe do not give these requirements but leave it to the owner (Have a look at ASTM E370) to specify the project specific requirements (otherwise each code would be the size of War and Peace and still would not cover everything!). With regard to cause for rejection high hardness can cause premature weld failures for example in pipelines in sour-service. 

hardness is not essential variable of most of the standard/code...
definately, hardness is an important factor when dealing with sour service or errosion.
that is why hardness is normally limited by project specifications / code...

For example: in sour service enviroment,
DNV limits hardness of carbon steel to be max 248HV10(root) 275HV10(Cap), 22Cr duplex max. 310HV10 and 25Cr duplex max. 330HV10.
NACE MR0175 ISO 15656-3 limits hardness of carbon steel to be max 250HV10(about 22 HRC), Duplex max. 25HRC (about 266HV10).

the higher the hardness, the better the resistance to errosion.

Someone please correct me if i'm wrong... thanks

Best Regards,
Noel Tan