[Ferro List] Fwd: micro-cracking, fibers

[Keith B]

Marc

A micro-crack in fc typically starts as a "Griffith Flaw" (kibitzers 
Google that for more info).  Flaws may or may not be tolerable depending 
on design and duty.  For OPC based mortars, if flaws are a concern, one 
mustn't forget that local tensile stresses may occur due not only to 
dimensional changes in early curing shrinkage, but also with longer term 
chemical changes and thermal change.  Given a Griffith Flaw, all you 
need is local tension exceeding the critical value at the crack tip for 
it to propagate, hence cracks creeping with aging, diurnal or seasonal 
temperature swings - and even when in an area not obviously under 
tension. I don't see Richard's PVA fibers as particularly useful for 
reinforcement, do see them of great value in cases where fracture 
toughness may become critical, but see them as priceless and unrivaled 
for general Griffith Flaw suppression in early cure. That's where most 
such flaws in concrete originate according to most literature I've 
seen.  They also might effectively raise the critical Griffith Flaw 
dimension at all ages. 

Flaws with surface expression might be healed by penetrating silicate or 
silane treatment, so, given the access to easily surface coat or treat, 
is microcracking critical even for something like a tank?  On the other 
hand, I have to take issue with  "mortar acts ONLY IN COMPRESSION".  
It's certainly true that the tensile strength of the matrix is 
conventionally ignored for calculations in RC design, but it's arguable 
at least that it matters, and certain that it matters for "advanced 
composites" being made or contemplated.  Many such are designed as 
intrinsically flawless or effectively so.

Your words about addition of high-modulus fibers to the cement-mortar 
matrix are well taken, though I think you meant "lower modulus" rather 
than "low modulus", high strength steel.  That said, more discussion may 
be useful.  Within a simple, tensile loaded composite section, 
comparative load sharing is in the ratio of the moduli.  That's to say 
the "fiber stress" of each component for a common strain is directly 
proportional to its modulus.  But that doesn't tell us which fails first 
- or what proportion (or absolute load) of the load on the whole section 
is being taken by each member of the composite.  Nor, for that matter, 
does it do much more than obscure the secondary stresses being developed.

Stretch a composite section, and, if it doesn't fail by secondary 
forces, the initial failure will be in whatever component first reaches 
its limit in STRAIN.  That property is independent of modulus.  It 
follows that, in principle, a lower modulus steel steel mesh with a 
lower strain limit would fail before a high grade steel fiber with both 
a higher modulus and a higher strain limit.  (In practice, it's further 
complicated by likely different behavior in the plastic range beyond the 
elastic limit.)  Further, even if the fiber had a lower strain limit, 
would its failure necessarily precipitate catastrophic section failure?  
It wouldn't, if there was sufficient reserve strength in the mesh to 
take up the added stress without exceeding it's strain limit.  This is 
mostly of academic interest though, because rational design almost never 
approaches the elastic limit with working loads...

That gets us back to considering the detail of load sharing, and at 
loads short of the obviously critical.   The load carried by each 
component is the product of its modulus and its cross section area, or 
proportionately, the product of modulus and proportion of the total 
section area.  If the matrix has a low modulus, the reinforcement a high 
one and a proportionately large cross section area, then indeed, we may 
assign most of the stress to the latter.  Typically though, in terms of 
proportional cross section, reinforcement forms only a small fraction of 
the section's area.  Further, matrix modulus is commonly measured as 
half or more of that of the reinforcement.  Why, then, do we neglect 
it?  The answer, from extensive and bitter experience, is flaws.  It 
only takes one crack to extend across the matrix and its strength 
becomes zero.  Clearly then, we can gain great advantage if we can 
eliminate matrix flaws and/or inhibit cracks from propagating.  In 
principle, that would let us utilize the strength of the matrix in 
addition to that of the reinforcement  -  or eliminate the reinforcement 
altogether. 

In first and early set, dimensional change is substantial and strength 
very low to moderate.  It follows that even relatively weak "short 
fibers" can act effectively to inhibit or limit incipient Griffith 
Flaws.  Later, when cure approaches completion, only fibers of modulus 
comparable to or higher than that of the matrix will be effective in 
inhibiting flaw activation.  Note that this action is not the same as 
inhibiting propagation of an established crack, nor is it necessarily a 
significant "reinforcement" action in its common sense.  Any gross 
tensile strength improvement seen primarily reflects preservation of the 
intrinsic matrix strength.  Several points follow:  There's little 
benefit to poorly made matrix material, because the flaws will be so 
common and extensive they can't all be suppressed.  Thin PVA fibers are 
great for early cure because they are so numerous for a given weight.  
They aren't so helpful at the higher stresses of full cure, because they 
are designed to slip, good for fracture toughness after matrix failure 
but of limited value to prevent that.  That's the reverse of steel fiber 
behavior, so a blend of both should be superior to either - and is.

The designed slippage of PVA fibers gets into issues of "secondary 
stresses".  Necessarily, if tress is applied to a composite with a 
relatively low modulus matrix with linear, high modulus reinforcing, as 
vi9a clamped ends, then shear must develop between reinforcement and 
matrix.  The stress is proportional to the load(s) and the area of the 
reinforcement, while the action of the reinforcement reflects its net 
cross section area.  It follows that, for a given section stress and 
mass of reinforcement, because a bar has a much smaller area than 
equivalent wire and fine fibers a drastically greater surface again,  
bonding shear stress is  large for a rebar,  much smaller for the wires 
of  FC  and far lower again for fine fibers.  Shear re. reinforcement 
bonding is one issue.  Another is section distortion and random fiber 
orientations.  Consider a compression load on a squat column.  Failure 
may be in shear, typically on a 45 degree plane, or actually in 
tension.  Poisson's Ratio relates to the degree to which a squat column 
bulges in the middle from compressive stress.  That means that its 
periphery increases, putting it into tensile hoop stress.  A mortar or 
concrete weak in tension may fail there despite apparent, perhaps 
measurable, high compressive strength.   Sections in bending or torsion 
may exhibit a failure mode of similar kind which might be inhibited by a 
significant random fiber content.

kb

Marc de Piolenc wrote:
> Dear listmates,
>
> I'm getting a little worried by some of the list traffic about
> microcracking and fibers, so I'm chiming in to remind us of some
> fundamental facts that seem to be getting lost in the discussion.
>
> Regarding microcracking, it is a given under load, but also nothing to
> worry about. Cured cement mortar has a high tensile modulus, but low
> tensile strength - hence it cracks under tensile strain. This is not a
> problem because, in ferro, mortar acts ONLY IN COMPRESSION. As long as
> the cracking stays "micro," there are very few applications that
> cannot tolerate it.
>
> Unfortunately, some people who regard it as a problem are advocating
> the addition of high-modulus fibers to the cement-mortar matrix, which
> completely defeats the purpose of the low  modulus, high strength
> steel mesh because load is never transferred to the steel mesh until
> the fibers fail - at which point failure of the complete composite is
> likely to occur catastrophically and without warning.
>
> In the very few situations where microcracking is not permissible, the
> solution is to use a slightly expansive mortar mix; this will preload
> the steel reinforcement in tension and even microcracking will not
> occur until the tensile preload is exceeded. A mortar that shrinks
> when curing is not acceptable in any ferro application, for obvious
> reasons.
>
>